Stéphanie Fonvielle

Argumentation-based Resolution of Ethos Conflicts in Educational Context

Before analyzing tension situations in an educational context, let us define the different concepts that help understand the disciplinary issues of our analysis: verbal conflict, argumentation, educational triangle. The latter refers to several complementary fields: anthropology, sociology, and interactional and argumentative linguistics.

State of the Art and Comparative Approaches

The verbal conflict can be defined with the help of various conceptual pairs: aggression and violence, relationship and conflict, negotiation and tension rise.

The verbal conflict: from aggression to communication breakdown

According to [START_REF] Lafon | L'agressif. Vocabulaire de psychopédagogie et de psychiatrie de l'enfant[END_REF], the aggressive individual is « celui qui est porté à attaquer, à provoquer la lutte, s'opposant à celui qui fuit les dangers ou les difficultés, et à celui qui cherche à comprendre et à concilier. ».

Agression is a disproportionate reaction to a situation, but does not automatically lead to communication breakdown. Violence, on the other hand, is a response that aims at destroying physically and/or verbally the other party. It thus corresponds to a failure of dialogue. It often arises in a conflict and has an impact on the relationship between the interactants in the conflict.

Fonvielle and Romain  Argumentation-based Resolution of Ethos Conflicts in Educational Context

« rapport inégal entre deux personnes, deux groupes, deux ensembles qui s'opposent au sein d'un même espace avec chacun pour objectif ou pour horizon non pas de liquider la partie adverse, et avec elle la relation elle-même, mais de modifier cette relation et tout au moins d'y renforcer sa position relative. »

A conflict may have a positive or a negative outcome: if communication is maintained, the resolution is positive and the tension at the source of the conflict is resolved; conversely, in case of communication breakdown, the resolution is negative and tension is exacerbated (Rey, Gomila & Romain, 2013). Thus, the conflict is a source of interactional progress as it contributes to the individual's development (Gibello 1990;[START_REF] Bondu | La recherche d'un accord : pour une éthique du conflit[END_REF]: the individual constructs his image from what he perceives of himself and of his opponent in the conflict. The conflict must be approached taking into account the interaction-associated phenomena. Goffman (1973, p 23.) describes the interaction as follows the mutual influence exerted by the participants on their respective activities.

In any interaction, the interactants show their own faces (Goffman, 1973ab, 1974 and take into account the others' faces. We will see later that this concept of face is framed in the notion of ethos in argumentation: it refers to the image that one projects of oneself and the image one has of the other person in his/her personal or professional life.

A conflict arising during interaction leads to tension. To defuse the tension and maintain dialogue, there must be a negotiation between the interactants. Negotiation is thus a process that helps manage the dispute (Kerbrat-Orecchioni , 2005).

To understand how a dispute process works, the interactional linguistics analyzes the various dimensions of the verbal conflict: the tension node(s), the process movement and the markers of tension. First, the tension nodes are threatening speech acts [START_REF] Austin | How to do Things with Words[END_REF][START_REF] Searle | Speech Acts[END_REF]: speech threatens the other's face. In educational setting, three forms of threatening speech acts (SA) can be used [START_REF] Schultz-Romain | La gestion discursive de la relation interpersonnelle dans la classe de français, Collection[END_REF][START_REF] Romain | Pour un modèle d'analyse de la violence verbale en situation scolaire ? Situations conflictuelles et relations interpersonnelles dans des classes de CM2[END_REF]Rey, Romain and DeMartino , 2013;[START_REF] Romain | Interactions conflictuelles et actes de langage menaçants en classe de la Language Education Policy and Peace 127[END_REF] : the "modest" SA containing threat alleviators ( for example one says " you should" instead of "you must ") , the "ardent" second order SA, based on an argumentative dynamics (for example one tries to convince the other to act) and the "ardent" first order SA that are just threatening ( for example one tactlessly gives an order). We will see how these tension

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nodes materialize in our corpus under study and how they reveal the image the teacher has of himself in the pedagogical relationship. Then, the verbal conflict also involves a movement that reflects the tension rise. This rise in tension was modeled by a French research group on verbal violence [START_REF] Auger | De la violence verbale : pour une sociolinguistique des discours et des interactions[END_REF][START_REF] Moïse | Contexte et violence verbale La mise en oeuvre des langues l'interaction, 4e colloque du réseau de sociolinguistique[END_REF][START_REF] Schultz-Romain | La gestion discursive de la relation interpersonnelle dans la classe de français, Collection[END_REF][START_REF] Carra Et Mabilon-Bonfils | Description de la violence verbale en situation difficile d'enseignement[END_REF]Fracchiolla Moïse, Romain and Auger, 2013;Rey, Romain and DeMartino , forthcoming , Rey and Romain, 2013;[START_REF] Romain | Interactions conflictuelles et actes de langage menaçants en classe de la Language Education Policy and Peace 127[END_REF]. There are four types of tension rise depending on the linguistic content: fierce, diverted, controversial and negotiated. A distinction can be made between the first three ones -not intended to threaten cooperation and communication (non-negotiated tension rises) -and the last one -allowing negotiation (negotiated tension rise). The first tension rise is called fierce as it involves explicit language and is an open and direct face threatening act ("You did a bad job"). The second one is called diverted because it involves implicit and indirectly threatening remarks ("You found the exercise difficult! Bastien found it easy, though"). The third one is named controversial as it discredits the other through charging discourses: ("You would have done better if you hadn't spent your time gaping and if you worked more seriously "). The fourth one is based on phenomena related to negotiation and cooperation to resolve the conflict ("If you want, for you to do better next time, during the break we will work on what you did not understand"). The threat is mitigated by the proposal for assistance and negotiation is now made possible.

Finally, the verbal conflict can be detected through various linguistic markers that relate to the relationship between the interactants during the conflict. There are two types of markers: those related to the position of each actor and those related to the relationship between the actors. The position markers point to a hierarchical or vertical relationship (use of injunction: the one who gives the order places himself in a higher position in relation to the one who obeys). The relationship markers demonstrate a willingness to engage in cooperative dialogue (use of personal pronouns: the case of the inclusive "we"). All these language tools will be used in the analysis of the content and the development of a teacher model. In this perspective, the argument provides an indispensable analytical framework for addressing tension, conflict and negotiation.

Fonvielle and Romain  Argumentation-based Resolution of Ethos Conflicts in Educational Context

Argumentation and Conflict Resolution

Argumentation is a field of linguistics in which conflict is considered as a linguistic and cultural practice. For a long time subordinated to the History of Rhetoric, argumentation has been given various definitions, among which:

-it is a linguistic method resulting in actions that are beneficial to society; -it is a logical Instrument determined by a set of mathematical laws; -it is a set of persuading figures of speech -it is a communication strategy aiming at gaining (actual or virtual) audience support.

The history of argumentation theory reflects the ideological, philosophical and rhetorical breaks which have gradually accompanied the term to the forefront of the political scene of the 21st century. Whether it is approached as an epistemological and philosophical subject in Europe or as a place where logical reasoning develops in the English literature, argumentation can be defined as a cultural practice anchored to a democratic ideal. The notion of debate is evoked as soon as argumentation appears in a situation of crisis. We refer to the conventional use of this term defined as a "usually animated discussion between interlocutors often with opposing points of view on a given topic" (TLFi). In the context of our

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interactional approach to argumentation in conflict situation, the debate guarantees the existence and continuity of the exchange: as long as the debate lasts, the problem can be solved. Conversely, in case of communication breakdown, the interaction is null and the argumentative strategy fails. This argumentation breakdown has been illustrated in History by some types of speeches that modernize a kind of nonexchange and thus fall outside the democratic process. For example, the pamphlet or propaganda speeches of the 19 th and 20 th centuries were based on mechanisms of criticism for the former and mechanisms of persuasion for the latter. Both favored the rhetoric of evidence and resentment that left no room for discussion: These types of speech may include "vexatious comments against a group or a person" (Moïse, 2012, p.8). They thus represent a context for a possible manifestation of controversial verbal abuse.

« […]
The objective of argumentation in conflict situations in an educational context is to maintain communication and the exchange of ideas, so that the learner can find a way out. The argumentation must be considered in its relation to the language and perceived as language practice. Thus, some French theories of argumentation report an argumentative dynamics demonstrating the interaction of the interactants involved in the debate. The argumentation will be either operation changing the other's beliefs [START_REF] Plantin | L'argumentation[END_REF][START_REF] Plantin | L'argumentation -Histoire, théories, perspectives[END_REF], distance negotiation [START_REF] Meyer | Qu'est-ce que l'argumentation[END_REF][START_REF] Meyer | La problématologie, « Que sais-je ?[END_REF], regulated cooperation [START_REF] Grice | Logic and conversation. Syntax and semantics : Speech acts[END_REF] or language function [START_REF] Bühler | Instigation to Aggress and Escalation of Aggression Examined from Personological Perspective: The Role of Irritability and Emotional Susceptibility[END_REF][START_REF] Danblon | La fonction persuasive[END_REF]. These definitions describe an argumentative interaction, i.e. the argumentation is part of a debate leading to communication. The distinction proposed by [START_REF] Amossy | L'argumentation dans le discours[END_REF] 2010a) between argument dimension and intention makes it possible to integrate the argumentation into language and to consider that all discourses are argumentative as they try to act on the opponent. In any event, there seems to be a consensus among all the argumentation theoreticians: (Plantin, 2001, p. 72).

This argument dimension leaves traces in the discourse that is produced. These traces for example illustrate the identity the speaker wants to provide himself with, the image he has of his interlocutor, the role and the place he gives himself in the exchange, etc. Here we can identify elements related to the interaction. These elements refer to concepts widely discussed by Aristotle in Rhetoric known by the name of ethos and pathos, but also to social schemes identified by the sociologist E. Goffman (1973). The updated notions of ethos and pathos will allow us to define the interactants in the pedagogic discourse, and to shift the scope of the conflict from the ego to the ethos.

Presenting Oneself in Educational Interaction and Educational Triangle

Aristotle's ethos establishes the difference between what the person really is and "the image the speaker builds of himself in his speech in order to make himself believable" (Amossy, 2010b : 25) . Another approach, borrowed from Goffman sociology (1973ab), defines the concept of ethos as "the construction of an image conducted within a specific social exchange" (Amossy, 2010b : 26). The influence of the social roles shaping ethos has to be considered here. With these two additional dimensions, ethos is now an essential tool for discourse analyses and argumentation studies. It is defined as presentation of the self (Ruth Amossy, 2010b). The issue of ethos or self-presentation is to be connected with both the interactional and argumentative dimensions of discourse:

« On adoptera donc ici une perspective résolument socio-discursive : la présentation de soi est sans doute un phénomène universel, mais elle ne s'effectue pas moins dans des cadres sociaux et institutionnels qui commandent ses modalités singulières. » (Amossy, 2010b, p.43) In this perspective, ethos will be determined in relation with a cultural framework providing a set of stereotypical representations. The existence of a collective imagination and of a cultural heritage shared by a same socio-discursive community asks for the definition of the stereotype as "a collective fixed representation, a cultural model that circulates in the discourse and in the texts" (Amossy , 2010b: 46) . Ethos is thus built

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from a repertoire of "stereotypical registers" in connection with established spheres (occupation, family, political inclination, religion, etc.). The professional ethos of a teacher is not the same as his ethos as a father or as a union representative. Drawing upon a common heritage, ethos can be built before the encounter with the person it is associated with takes place: one can have a preconceived opinion of someone else thanks to or because of these shared different registers. This so-called pre-discursive ethos refers to "the preliminary image the audience has of the speaker as a function of his status, reputation or previous statements" (Amossy , 2010b : 72). In any event, these two modes of ethos construction play a key role in social interactions: "the appropriation of the stereotypical image of a social category is essential both in terms of construction of identity and in terms of effective communication " (Amossy , 2010b : 44). How can this concept of ethos be understood in an educational context?

The didactic triangle is defined as a system involving two actors -the teacher and the learner -bound by knowledge to be transmitted. The terms used to refer to these two actors refer to their functions within the didactic triangle: the teacher passes on knowledge, and the learner assimilates this knowledge. Two kinds of ethos must be built: that of the teacher and that of the learner. At the heart of the didactic triangle is what we have chosen to call the soul, which helps refer to cultural phenomena involved in and through the educational act. In our analysis, this soul refers to the collective cultural representation shared by the actors. It is therefore the pool of stereotypes at the disposal of the teacher, so that he can build his professional ethos, and of the learner to build his ethos as a pupil in the class and in relation with the teacher. Thus, the teacher builds up his educational ethos by drawing from this pool of stereotypes. The language interaction will influence how the stereotypes are -consciously or not -chosen and how their form may change as the exchange proceeds. Ethos plays an important role in the educational community in that it gives the actors a particular posture, i.e., an inter-relational role influenced by sociological constraints set by stereotypes. According to [START_REF] Charaudeau | Le contrat de communication dans la situation de classe[END_REF], the teacher-learner relationship relies on an implied communication contract whose aim is the transmission of knowledge. Conventionally, the teacher, since he has the knowledge and is responsible for his class and his lessons, occupies a high/dominant position while the learner is in a low/dominated position since he has to listen to the teacher, obey his orders and follow his advice and recommendations.

In this chapter we have presented the concepts, tools and analytical framework necessary for the study of the rise in verbal tension in an educational setting. We will now show how this tension rise occurs in extracts of educational interactions.

Identification and Analysis of Tension Rise Phenomena

We will present excerpts from studies conducted in schools, from nursery school (3-10 year old children) to junior high school (11-14 year old school students). These schools are all located in the south of France and belong to differentiated institutions. The interactions studied and presented in this paper were collected throughout the school year. They illustrate the processes of negotiated and non-negotiated rising tension and exemplify two forms of conflict management. We will give an example of each case and we refer our reader to the annexes for other examples.

Case of a negotiated rising tension process

Nursery school (4-year-old pupil)

-Zone violence/Réseau Ambition Réussite, Marseille --school specially endowed to face violence in disadvantaged neighborhoods:

[one morning, while the children are hanging their jackets on the hooks and getting into the classroom, the nursery assistant calls on a pupil, who has behavior problems

Context of the Exchange

The teacher is called in by the nursery assistant who informs her that she has just been insulted by one of the pupils. The teacher, who was not present when this happened, goes to the hallway to discuss with the pupil. He is standing in front of his hook and the pupil's picture above the hook next to his is at his feet. The teacher decides not to speak about the insult but to ask the pupil to put the picture back on the wall above the hook, and to make him speak about what has just happened. The pupil has had recurrent behavior problems in the classroom and the teacher tries to interact verbally with him.

Dynamics involved in the process of tension rise

First level : Injunction

In the hallway, the teacher starts by asking the pupil to explain or to talk about what has just happened. As he does not react, she formulates an injunction "we are going to have to stick the picture back above the hook." This injunction, which brings a constraint threat to the face of the pupil, is mitigated by the use of an impersonal form and of a modalization ("we are going to have to" vs. "we must"). The pupil refuses the injunction ("no / no").

Second level : Reformulation and Negotiation

The teacher then reformulates the injunction accompanying it with a threat, warning the pupil against his refusal to mend (" if you don't want to help me + we will have to take your picture down too". At the same time, she produces a hypothetical formulation "if ... we will also have to..." with which she positions herself alongside the student in the reparation process (the "you" to the pupil next to the "help me" which refers to the teacher) and where the sanction is again announced using Conflicts in Educational Context an impersonal form "we will have to take your picture down too". Note that here the simple future replaces the near future, giving the pupil additional time (for reflection?) which goes together with the "if you don't want to help me", which makes it possible for the pupil to refuse but make him liable to punishment. Linguistic politeness works here as a repair marker for the attack to the pupil face (and at the same time protects the face of the teacher from a refusal by the pupil who will therefore be punished). In the end, the pupil, helped by the teacher, puts the picture back above the hook

Third level : Verbalization

Then the teacher again tries to make the pupil speak by asking him about his emotions and about the interaction with the assistant (" why are you upset? + + what happened? "). She uses her own words to express the emotion felt by the pupil (anger) and suggests that he should try to explain, in his own words, what led him to insult the assistant and to tear off the picture of the other pupil. Through mimics and gestures of drawing on his jacket, the pupil draws the attention of the teacher to his jacket -which is why the tension rose (the assistant asked him to take it off but he can't). The teacher then explicitly verbalizes the situation "you cannot remove your jacket," which leads the pupil to verbalize his emotion:" it gets on my nerves": he is now able to use words. We note here that up to this point, words have failed him in the expression of the situation and of his feelings: he could not do it or he did not want to do it. The teacher then offers to help him take off his jacket, which leads the pupil to say "no / I want you to close it for me". What comes next makes the teacher understand why he has asked that. Once the zipper pulled up, the pupil unzips his jacket and is able to take it off at last.

The Logic of a Positive Negotiation

Three levels can be observed from communication breakdown to communication resumption. At each level corresponds to a different strategy: injunction, reformulation and negotiation, verbalization. The teacher begins with the injunction, and then, seeing that the communication is broken down, she reformulates her injunction and uses negotiation tools. She manages to restore communication and

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provide a positive solution to the conflict through cooperative verbalization.

To develop a negotiation with the pupil, the teacher first uses position markers, mainly in the first level. She then uses relationship markers that ensure the successful outcome of the conflict and a reduction in tension.

In this negotiated rise in tension, the teacher uses ardent second degree speech acts in order to obtain the cooperation of the student.

Illustration of a Non-Negotiated Tension Rise Process

Primary school final year (10-year-old pupil) - T: [she finishes writing in the book, then she gets up and goes to the back of the classroom to throw the book on the pupil's desk: to be signed for tomorrow.

Context of the exchange

Here the situation is the same as in the previous example. The teacher could not witness the aggression by the pupil but she hears the story from another pupil.

Logic of a Non Negotiated Rising Tension Process

Unlike in the previous example, there are no logical disparities in the teacher's discourse: it is therefore impossible to determine different levels. The teacher's verbal behavior in fact responds to one and the same logic that leads to the impossibility of a negotiation with the pupil.

The teacher immediately initiates a tension rise, successively fierce (e.g., " ! Shut up ", "on my desk ", "your book on my desk "), controversial and diverted e.g., "so ↑ you did not touch him / you did not you touch him + so he hurt himself by himself↑", " so, nobody hit him "), between the two pupils reported as being responsible for the aggression against a third pupil. Her intervention is pointed essentially to one of two students who will protest of his innocence several times and will therefore contradict the teacher. At no time, she uses a negotiated tension rise like in the first example. Her speech acts are injunctive and aim at making the pupils acknowledge their responsibility and ultimately punishing them by asking for their report book. The markers she uses are only position markers. It should be noted that the pupil, in return, produces a fierce response by presenting a defense built around negative assertions (e.g., "no", " it's not me ", "I didn't punch him "). He finally gets tired of the tension rise ("I won't say anything"). It should be noted that the pupil, in return, produces a fierce response by presenting a defense built around negative assertions (e.g., "no", " it's not me ", "I didn't punch him "). He finally gets tired of the tension rise ("I won't say anything").

So we have two different examples of conflict management in a class: in the first case the teacher changed her strategy and negotiation became possible, while in the second case the teacher did not change her initial

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strategy and so protracted the conflict. This restrictive approach contributes to the rise in verbal tension up to the point of no return. We will see how this choice reflects a position that can be defined in terms of ethos.

Teacher's Ethos & Non-Negotiated Tension Rise

Teacher's ethos expressed through words: his master's voice?

The teacher's discourse bears the traces that help rebuild the ethos he/she adopts and thus proposes to the learner. Different sets of linguistic clues emerge, making it possible to assemble the characteristics of a teacher ethos based on injunction, hierarchy and empowerment. These identity dimensions intervene in the teacher discourse in a variety of ways. Firstly, they are recoverable directly from the teacher talk, as they leave traces in the verbal material of teacher talk. These traces reveal an ethos in an imperative model. Secondly, they belong to the enunciative modality selected by the teacher. This reveals the didactic position the teacher wants to occupy in the face-to-face opposing him/her to the learner. In this perspective, the markers are no longer to be found in the discourse itself, but in the kind of discourse that the teacher has chosen. Finally, the language used by the teacher places the vision he/she has of the relationship with the learner within the scope of empowerment.

An Imperative Model

As was seen in the analysis of the corpus, the teacher favors an educational model based on injunction. She uses in her discourse all the features of the imperative style, manifested in the use of the tenses and of the different structures to give an order. Various clues emerge that express the more or less identifiable injunctive intention of the teacher talk. The imperative is the perfect injunctive mood, it is the mood used in "Shut up!", "Hurry up" and "Stand up straight", by which the teacher gives an identifiable order to the learner. This is perhaps the most "aggressive" mood in verbal communication as it means that absolute

Fonvielle and Romain  Argumentation-based Resolution of Ethos Conflicts in Educational Context

obedience is required from the learner. The imperative alone illustrates what "giving an undisputable order" means, i.e., the learner has to respond with a physical action rather than just with words (as opposed to a dialogue that will wait for a response, for additional information). The teachers in the corpus under study also use other structures based on injunctive intention, as for example: "either you say it out loud or you shut up," "you read louder or you go sit down" "you stay in your " give me your report book", "turn around", " hand me your report book". Finally, one last verbal form omits the verb, which increases the injunctive dimension of the teacher discourse: "on my desk" "your report book on the desk."

Several remarks should be made here in connection with this imperative style. First, imperatives or phrases all refer to orders concerning actions related to either the verbal activity of the learner such as "shut up", " say it aloud " or "read louder" or his behavior " you stay in your seat" " you go and sit down" " you turn around " " stand up straight" "hurry up" "you give me your report book". The Injunctive talk of the teacher is thus centered around two poles: speech and gesture. In the first case, speech is not allowed and when it is allowed, it is highly constrained (" out loud "). This injunction reveals an aspect of the ethos of the authoritarianism of the teacher, who sees teaching unilaterally: the teacher gives orders, the learner complies. This vision is summarized in the second text by the teacher as follows: "I need you to listen and to keep quiet." Moreover, using the same authoritarian strategy, the teacher sometimes integrates her injunctive forms in an alternative exclusive system of the type" either/or ": "either you say it out loud or you shut up", " you read louder or you go and sit down". Then, a reference to an object prototypically linked to education helps establish the ethos of the authoritarian teacher: this object is the report book. It is a symbol of authority but also of punishment. In this context, the tool of repression that the report book is defines the ethos of the teacher, as for example the baguette is a symbol of the French or the gown a symbol of the lawyer. It is through this symbolic object of punishment that the teacher will build an ethos rooted in the stereotype of authority and punishment. This symbol of authority takes on an additional implicit dimension and helps reveal the hierarchical structure existing in the educational system.

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Hierarchical Argumentation

This hierarchical structure of the educational system can be perceived through the enunciative modality of the teacher who uses repeated ironic comments. The latter, as we have seen, are an illustration of polemical violence. Examples of teacher ironic comments about what the pupil says are numerous in the corpus under study. By his comments, the teacher places himself in a hierarchical position of superiority that allows him to look down upon the pupil. Two general trends are visible in the teacher talk, which illustrate a sometimes humiliating form of condescension. First of all, the teacher reiterates what the pupil has said, emphasizing the absurdity of the utterance. This is the case of the following:

-So you did not touch him, you did not touch him, so he hurt himself by himself -And well it's me of course who hit him -I dreamed that? I'm hearing voices today

The argumentative pathway is part of a dynamics ensuring the passage from a given -"you did not touch him", "you did not hit him ", "this did not happen" -to a conclusion -"so he hurt himself by himself", "it is me, of course, who hit him", " I' m hearing voices". The passage from the explicit data to the conclusions is indicative of the ironical intent in that, every time, the teacher favors an absurd conclusion: the possibility that the pupil hurt himself, that the teacher hit him or hears voices, is null, a priori considering that they are sane-minded persons. It is this impossibility that gives the conclusion enunciated by the teacher its ironic dimension.

Then, the teacher ridicules the pupil's attitude, either by caricaturing a behavior as when it refers to the poor motor coordination of the pupils ("why, when you raise your hand, do you open your mouth ? "), which relegates them to the level of the "simple -minded" or by imitating the reaction of the pupil ( "well, what's wrong?") with a mocking tone. Note the importance of non-verbal communication, which makes it possible to capture the passage from the interrogative prosody used by the pupil to the mimic-gesture that ridicules the question asked by the pupil. Finallyanother possible way of ridiculing -the teacher this time starts from a positive situation -the pupil has done his homework -to indirectly emphasize its negative-because-exceptional character : " it' s going to

An Overpowering Register

The teacher develops a register that could be associated with overpowering the other, in this case the learner. As we have seen, she uses several imperative addresses against the learner that she also tries to control by using a sometimes humiliating discourse. The register that the teacher prefers can also provide clues about how she perceives herself, at least how she perceives her own role and position as a teacher. Many imperatives or ironic comments come with a formulation from familiar language register, as in for example "you fucking kicked somebody who was already on the floor," "when he lets me say something," "I don't care ", that are from a colloquial, even coarse language register. The language registers used are representative of how one sees the other and of the position one takes vis-à-vis the other in the interaction. We can think of the language registers determined by an everyday life situation, such as the Javanese registers, or else of the overcorrection phenomenon that shows a willingness to adapt to a register that is not usually used. The language register illustrates the image one has of the other: by adapting one's language to the other' register, one reveals the image he has of the other. As for the teacher, we assume that she masters various registers, at least the common French register. In the cases under study, even if the teacher uses an oral style, she also often makes use of words borrowed from the coarse French register -words that she should not use in the context of the classroom. She uses them to show her opposition to the attitude of the pupil that she considers impertinent or at least that does

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not comply with the imperative or hierarchical model she follows. The teacher uses this register to move into the "aggressive" space of the learner: the war of position can begin.

This war about ethos and space is illustrated by the use of personal pronouns.

Teacher Ethos versus Class Group Ethos

The personal pronouns, what they refer to and what they are used for in interaction, provide an indication not only on role management within the didactic triangle but also on the vision of the self, of the other and of the class group. Empowerment and conflict strategies can therefore also be perceived here. Three pronouns will arouse our interest, "he", "we" and "you"1 . The personal pronoun "he" is used for the third person singular. Contrary to the first and second person singular "I" and "you", "he" is absent from the direct interaction, which makes it a "non-person" pronoun ( Benveniste ) : it is the prototypical pronoun in history enunciation, where "personne ne parle […]; les évènements semblent se raconter euxmêmes" ( Benveniste 1966, 241).

In contrast, "I" and "you" make it possible to identify the interactants in a discourse enunciation "où quelqu'un s'adresse à quelqu'un, s'énonce comme locuteur et organise ce qu'il dit dans la catégorie de la personne" (Benveniste 1966, 242).

In the context of the verbal interaction, the two pronouns "I" and "you" refer to the speakers present and active in the conversational exchange. These pronouns used in that way punctuate the teacher talk. However, a familiar use (Riegel , Pellat and Rioul , 2009 : 366) of the personal pronoun "he" in the verbal interaction reflects the teacher's will to exclude the learner from the conversational space, i.e., to deny his quality of potential speaker and thereby to exclude him from the exchange: "when he let me say something, I may be able to tell him what's wrong."

Using the third person personal pronoun to speak about a speaker that is present in the conversational space, the teacher infringes the rules of polite discourse that acknowledge the presence of the other in the conversational space. This exclusionary use of the personal pronoun reflects the distance that the teacher wants between her and the learner. The use of the pronoun "we" is also interesting in our instances. The pronoun "we" can take on different values depending on the context , with a base value which is "that of an indefinite pronoun referring to a person or a group of variable size of persons that the speaker cannot or does not want to identify more accurately " ( Riegel et al , 2009 . 364). It can function as a substitute for all the personal pronouns "rejecting what they refer to in anonymity" (ibid. ). The teacher makes perfect use of these shades of meaning of the anonymizing pronoun "we". In the first case, the "we" refers to the teacher in association with her class: "If you want, we go and leave you". With this "we", she opposes a collective ethos, which he represents, and the two other pupils, to whom she refers with an excluding "you". In addition, the following passage is interesting in that it is not always easy to recognize the values of the different "we": In "we are trying to explain" and "we are working" the personal pronoun is opposed to a "you", as in "you are flirting with Aya". Again, the "we" refers to the collective class/teacher ethos. Nevertheless, we can wonder what value to assign to the first "we": does it refer to the teacherindividual ethos -or to the group -collective ethos? In the first case, the use of "we" instead of "I", means that "the speaker refers to himself while blending into the anonymous mass referred to by the indefinite form" (Riegel et al. , 2009 : 365). The distinction is not obvious. It is even less obvious in the rest of the passage. The "we" in "we are wasting our time" can refer to two troublemakers, the collective ethos or the individual

Language Education Policy and Peace 121

ethos. In the first case, designating the other with "we" instead of "you" "undermines the direct relationship that [this] pronoun establishes between the speaker and his interlocutor(s)" (ibid.). The use of personal pronouns contributes to excluding learners in difficulty either by rejecting them out of a collective ethos representing the class and the teacher or by denying their role of speakers by referring to them with "he or "we". In all cases, the distance is established.

The word marks in the discourse of the teacher make it possible to build up the ethos that he/she favors. An authority figure, who has a strong intellectual capital allowing him/her to overpower the learners, in particular through his/her position in the group to exclude troublemakers. These strategies correspond to a vision of the smooth running of the educational system: if the roles/positions are respected), the system works, while if the roles/positions are not respected, they should be re-established. This is a pre-requisite for our remediation hypothesis.

Ethos Remediation: Perspectives

To conclude, let us consider again the situations of verbal abuse using the notions of ethos as a remediation tool. We will see that one of the possible explanations for the rise in verbal tension should lie in the predictability of the concept of ethos that teachers should avoid. In other words, surprising the expectations of the learner in difficulty should help maintain contact.

Communication Breakdown due to Ethos Conflict / Prior Ethos / Stereotypy

We have seen that the teacher presents through her discourse an image of herself based on the figure of authority and hierarchy. This is a historically motivated stereotype as it comes from the figure of the Schoolmaster of the French Third Republic, whose role was to train future citizens along the republican and secular values .The gray smock and the ruler represented the attributes of this tough but fair schoolteacher. This image is deeply rooted in the collective imagination and some features do not fade with time. If we contextualize within the frame of our voltage rise, we note that the breakdown occurs around this figure, or more particularly around the characteristics associated with the master's figure: his authority. The imperatives and other enunciative the teacher and the learner reveal a teacher discourse far from the discourse of an authority figure favoring unilateral interaction. The teacher plays the card of proximity and support to the learner. This construction of ethos is characterized by specific speech acts supporting the maintenance of the teacher-learner interaction, the inclusive and particularized use of pronouns and addresses to the learner, the spatial rapprochement that gradually brings the pupil closer to the teacher. In the first case, the teacher favors questions that motivate the act of exchange over acts of injunctive language to maintain verbal interaction. Thus, following injunction revealing a mostly dominating ethos, the teacher starts the dialogue with the learner with the partial and direct questions: "what happened?", "why are you upset?", etc. . In the second case, she constantly manifests her attention to the learner by using an identifying "you", contrasting with the excluding "he/him" used earlier.

The pronoun "you" is not used to exclude the pupil from the rest of the group, but rather to integrate him as a person who can join the group with the help of the teacher: "I need you, I need you to listen to me, to be quiet like the other children". The use of the pronouns illustrates this integration to the group by an endless coming and going between the teacher -"I" -, the learner -"you" -and the "we" of the collective ethos that includes the learner: "When you speak, when we are all together here". This reduction in the distance or proximity effect is also reflected in the spatial rapprochement which could in itself summarize the attitude of the teacher: "Do you want me to sit you down on a chair next to me?"

The report book has been replaced by the chair that now enables the pupil to find his place in the group, i.e., to rebuild his ethos on contact with that of the teacher. The teacher plays with the class design by offering the learner to distinguish himself from the group and at the same time get closer to her. We note that the tension rise is prevented thanks to the change in ethos, from an ethos of the authority to an ethos of the exchange and rapprochement symbolized by the chair positioned near the teacher.

This raises several questions that should not be minimized in interactions in an educational context: first, the question of the deliberate choice of the ethos, and, more specifically in the context of the interaction, the question of whether there is manipulation. Manipulation is defined as a strategy aiming at making the other act unknowingly. Different attitudes are then possible, such as seduction or "emotional" [START_REF] Sperber | La pertinence. Communication et cognition[END_REF]. En effet, ses interventions sont en adéquation avec le cadre interactionnel pré-établi par elle-même et ses élèves en début d'année (et rappelé régulièrement) (cf. travaux de [START_REF] Goodwin | Conversational Organization : Interaction between Speakers and Hearers[END_REF] et [START_REF] Clark | Using language[END_REF] visant l'adaptabilité du discours au contexte interactionnel ; et ceux de [START_REF] Schegloff | The routine as achievement[END_REF]

108 Fonvielle and Romain  Argumentation-based Resolution of Ethos Conflicts in Educational Context

	« la limite du concept d'argumentation est atteinte seulement
	lorsqu'on sort des pratiques langagières : hypnotiser n'est pas
	argumenter. »

  zips it up and goes with the child towards the classroom. On entering the classroom, the child unzips it, and takes it off by himself]

	Language Education Policy and Peace 111
	[the pupil looks at his jacket and pulls on it]
	T: you can't take your jacket off
	P: it bugs me
	T: do you want me to help you
	P: no / I want' you to zip it up
	[the teacher
	P: no / no
	T: if you don't want to help me + we'll have to take your picture down
	too [they put it back up together, without a word. Then the teacher
	stoops to his level, she's facing him and asks]
	T: why are you upset ++ what happened

, Samir] A: come on Samir/ hang up your jacket and come to class P: leave me alone big cow (he tears off the picture above the hook next to his and throws it down on the floor) T: what happened ++ we'll have to put it back on the wall

128 Fonvielle and Romain  Argumentation-based Resolution of Ethos Conflicts in Educational Context

  : parce qu'on fait des bêtises… non ::: <Samir baisse aussitôt la tête : le ton de l'enseignante baisse davantage, le rythme est encore plus lent> on vient en classe + pour faire + et découvrir + des choses + pour chanter + taper dans les mains + pour faire des dessins <elle montre les ateliers> + pour faire des canards et quand on est là + sur le banc ++ qu'est-ce qu'on fait E : on ne fait pas de bêtises P : on ne fait pas de bêtises + et on écoute des histoires + tu sais + quand tu parles + quand on est tous ensemble assis ici <Une longue pause intervient. Il ne la regarde que lorsqu'il parle. Sinon il regarde en face ou sur les côtés et en hauteur.> P : ça me gène ++ donc je ne peux pas apprendre aux autres enfants + les chansons + lire les histoires +++ <il baille, pause, il regarde son collier> alors tu sais ++ si tu as des choses à me dire + tu peux me parler + est-ce que /// alors qu'en je suis assise ici <elle met sa chaise à l'endroit même où elle la positionne au coin regroupement> +++ est-ce que tu veux que je te mette un chaise à côté de moi <son regard se pose sur la maîtresse, il soulève la tête, il sourit et répond calmement> E : oui P : parce que j'ai besoin de toi ++ j'ai besoin que tu m'écoutes + et que tu sois <il glisse de la chaise> sage et que tu écoutes comme les autres enfants/ d'accord E : oui 2 Corpus Romain, Romain (2010), Rey et Romain (juillet 2013). : et si je mets la chaise là <elle déplace la chaise qu'il a laissé vide puisqu'il est toujours à terre> +++ est-ce que tu écouteras mieux E : ou ::i P : on essaye < ton interrogatif > on essaie/ demain/ matin ++ ce sera TA chaise/ regarde <elle la montre>/ la chaise de Samir 3 L'enseignante s'entretient avec un élève qui parasite régulièrement ses interactions. Elle le fait en dehors de la présence des autres élèves. Elle lui rappelle le rôle de l'école et le fonctionnement des interactions en grand groupe. Elle ménage la face de l'élève en recourant à des A.L. ardents de second degré qui atténuent la menace portée à la face de l'élève en argumentant sur le fonctionnement coopératif des interactions verbales en classe (M.T. argumentative visant la négociation positive et coopération). Taxèmes de relation (« j'ai besoin de toi », « on ne fait pas de bêtises », « quand on est tous ensemble », « on essaie », etc.). Elle convoque les principes de coopérations linguistiques (cf. Grice, 1975 : maximes de quantité « n'en dites ni trop ni trop peu » ; de qualité « ne dites pas ce que vous croyez être faux » ; de relation « soyez pertinent » et de modalité « soyez clair ») et le principe de pertinence

	Language Education Policy and Peace 129
	P : tu ramasses A.L. menaçant ardent de premier degré exclusive
	d'argumentation (M.T. fulgurante). Taxèmes de position (« tu »,
	injonction dans le contexte d'une relation verticale).
	E : non Réfutation
	P : si + tu ramasses/ sinon c'est puni/ tu le sais/ on ne jette pas les livres
	<il ramasse le livre> A.L. menaçant ardent de second degré -
	inclusif d'argumentation-(M.T. argumentative à visée de
	négociation positive et de coopération). P ne traite que le premier
	noeud de tension (l'injonction réparatrice) et non le second noeud
	(le refus de réparer). Taxèmes de relation (« tu, on », rappelle des
	règles connues et acceptées par tous après discussion, etc.). 2
	1.2
	P : est-ce que tu sais pourquoi on vient à l'école
	E : parce qu'on fait des bêtises

P P

Classe de 6 ème (élèves âgés de 11 ans), cours de mathématiques -Zone d'éducation prioritaire-Réseau Ambition Réussite, Perpignan-

  sur la co-construction du discours). Ce cadre n'est pas rappelé ex-nihilo mais est mis en dynamique à la fois avec la situation posant problème (l'élève interrompt régulièrement l'enseignante), avec l'expression des émotions de l'enseignante (« ça me gène +++ donc je ne peux pas apprendre aux autres enfants ») et tout en donnant la parole à l'élève tout au long de l'échange et en s'abstenant de l'interrompre ou de chevaucher ses propos. Elle le fait participer, elle co-énonce avec lui l'argumentation qu'elle conduit et elle convoque la multimodalité de la parole (elle est proche de l'enfant, à sa hauteur, elle recherche son regard, elle baisse le ton de sa voix et ralenti le rythme et le débit de sa voix). P : moins 20 pour le point C c'est bon alors David tu vas continuer pour le: vingt-quatre (toux) // tu mets à côté tu traces un trait vertical / juste à côté tu traces un trait horizontal oui allez tu mets numéro vingt-quatre sur la même page / (on frappe à la porte) entrez / merci < … ? > / tu me donnes ton carnet A.L. directifs ardents de premier

	2.

Michaud (2009: 24) points out that conflict would be :

In French, the pronoun « on » is used and can't be translate in English. "On" refers to "je" ("I"), "tu" ("you"), elle/il ("he/she"), "nous" (we), "vous" (you) and ils (they). The translation in english doesn't allow an analysis of each nuance in French language.

Corpus Romain, Romain, 2010.

Corpus Lorenzi, Romain et Lorenzi, 2013

Conflicts in Educational Context

rain tomorrow ." These speech acts that the teacher uses to ridicule or humiliate the learner are "domination-oriented disparaging speech acts" (Moïse, 2012, 8).

By favoring reductio ad absurdum argumentative reasoning and by using a mocking discourse, the teacher considers her relationship to the learner as a distance and hierarchy relationship: she overpowers the learner by undermining his ethos -highlighting the fact that he does not often do his homework. The teacher builds up and asserts her ethos as well as her position in the educational model by underlining what confines the pupil to a submissive position of learner. Can we see here strategies of violence? The register used by the teacher may provide a last interesting indication. Conflicts in Educational Context modalities are rejected by the learner who expresses his opposition by his attitude, by his words or by his tone. Therefore, the teacher and the learner -consciously or not -share the same cultural reference, the former stating it and the latter rejecting it. Thus, the tension rise could be discussed in terms of shared ethos: for confrontation to occur, the ethos must be interpreted by the learner and must refer to a shared cultural model, likely of course to evolve over the years. The difference will only concern the acceptance or rejection of the ethos projected by the teacher: the class adheres to this ethos -it is the "we" of the collective ethos, the learners in difficulty reject this ethos -it is the excluding "we."

In the case of the shared ethos and stereotypy, we go further and believe that the notion of prior ethos plays a fundamental role in this ethos war. Prior ethos means the a priori representation that one has of another person, organization, party, institution, etc. In the context of school education, we assume that the figure related to the authority is prime: the learner expects to meet with a representative of this authority figure. In this perspective, it is this prior ethos that the learner opposes so that he can build his own ethos in the classroom -the rebellious pupil or the pupil opposing the master. It is for this reason legitimate to wonder what image of the prior ethos of his/her pupils the teacher has. If we consider the tension rise in line with the notion of prior ethos, and define it as in contrast with ethos, then we suggest that this tension rise can be alleviated by changing the ethos. It is this strategy that has been chosen by the teacher in the situation presented in the next section.

Remediation Adapted to the Ethos

We find in these examples the figure of authority and hierarchy that was present in the previous teacher discourses. The teacher uses the imperative mood (" we will have to put the picture back above the hook", " you pick it up"), alternative formulas with "if" (" if you do not want to help me, we will have to take your picture down"," pick it up, or you'll be punished") , the evocation of the sanction ("punished") , and the use of the personal pronouns "I", "you" and "we". Nevertheless, in the first three cases the ethos is temporary, diffused, and with a different scope from the ethos of the authority. Indeed, authority is only a component of the ethos favored by the teacher, who gradually changes her ethos to adapt it to the reception by the learner who is opposing. The exchanges between Conflicts in Educational Context blackmail, which we could see in the responses of the teacher (bring the chair closer; if you do not do this, I could not teach; change in tone from the imperative to the question).

The knowledge of the different ethos helps manage the negotiation of the tension rise and avoid the final communication breakdown. Hence, this dimension should be an integral part of education for teaching, which, to our knowledge, has not been the case so far. Thanks to a better control of the image of the teacher, related to our cultural heritage, the ethos war will not happen again.


Peter Leifer Or-Aqiva

The Quantum Relativity and Dynamical Spacetime

Keywords: PASC: 03, 65 Pm, 03, 65 Ca

published or not. The documents may come

1 Introduction E. Schrödinger and A. Einstein discussed the principle difficulties concerning the notions of particles and acceleration as fundamental entities in the modern physics about 70 years ago [START_REF] Schrödinger | [END_REF]2]. The mist of probability partly hides these fundamental difficulties. But the fundamental questions have no answers up to now [3].

The deep rooted assumption about existence of isolated system such as "body" or "particle" is very contradictable even in the framework of the elementary quantum physics since, say, a free electron has indefinitely large size due to the plane wave 1 function and, hence, cannot be "isolated". However, it is impossible simply discard this intuitively absurd result since the plane wave solution of the Dirac equation leads to the nicely confirmed the dispersion law on the "mass shell". This is the simplest example of the fundamental unsolved problems related to the localization, divergences, etc., [START_REF] Leifer | The relativistic non-linear quantum dynamics from the CP (N -1) geometry[END_REF][START_REF] Leifer | The Quantum State-Sependent Gauge Fields of Jacobi[END_REF][START_REF] Leifer | The Project of the Quantum Relativity[END_REF].

The classical "body" or "particles" and their abstract model -"material point" cannot be used as a primordial elements of the consistent QFT. The distance between bodies -the root mathematical discriminator of classical physics is very vague parameter in quantum theory. The second fundamental classical primordial element is the "force" as some external relative to the "body" factor capable to change the body state -its coordinates and velocity. Quantum theory hides the "force" in a shadow since the reason of the perturbation of quantum motion is not a force but the EM potential changes momentum p = m v in the additive manner P = m v + e c A. It turns out that the nature of momentum and potential requires to take into account the fundamental symmetry of interaction and in fact a new geometry of spacetime as it was in the case of the Maxwell electrodynamics leading to the relativistic mechanics of Einstein. The Scrödinger picture even in the case of the relativistic Dirac equation is quite acceptable on the atomic level but its continuation down to the sub-atomic (nuclear) level in very questionable. Probably, the long living attempts to attribute the universal spacetime environment for any "elementary" particle like electron may be a fundamentally wrong. Such embedding of particles into pseudo-Euclidian (or pseudo-Riemannian) single spacetime seems to be so obvious and absolutely natural that even some doubts look like a mockery on the common sense. Nevertheless it is worse while to take into account that our every day experience even with modern scientific background is mostly mesoscopic and just the microscopic and global picture of the world are controversial. But up to now physicist's majority assumes that the relativistic symmetry is enough restrictive (besides GR) in order to build correct QFT (in the spirit of SM and even beyond it). This is one of the most erroneous assumption in modern physics.

In order to see this more clear it is useful return to classical mechanics of Newton where physical parameters and geometrical values are perfectly separated (in QFT such separation is questionable). Say, in the second law m d 2 x dt = F acceleration is pure geometric object (vector) whereas the mass is a scalar physical parameter. All is good if one deals with pointwise particle or absolutely solid body. Then given empirically mass of the body and its shape together with applied force and moment define the acceleration and trajectory. If a body, however, is deformable under the action of the external forces or in the case of the "falling cat" motion, then the dynamics will be more complicated and requires essentially new gauge theory of finite deformations [START_REF] Littlejohn | Gauge fields in the separation of rotations and internal motions in the n-body problem[END_REF]. Applying this apparatus in QFT one shall remember that there is essential simplification in the classical case in comparison with the QFT. Namely, one may be sure that the macroscopic rods, masses, etc., move in 3D Euclidian space, whereas in the QFT case there are serious doubts in the motion of quantum states of single "elementary" particle in the 4D pseudo-Euclidean or pseudo-Riemannian spacetime. Shortly speaking -initially one should forget about "particle" and think about the motion of the quantum state in some functional space.

The intrinsic unification of the quantum theory and relativity is possible only on the way of the serious deviation from traditional assumptions about a priori spacetime structure and the Yang-Mills generalization of the well known U(1) Abelian gauge symmetry of the classical electrodynamics. In fact, more general gauge theory should be constructed. Formally we deal with the quantum version of the gauge theory of the deformable bodies -the gauge theory of the deformable quantum state. More physically this means that the distance between quantum states is strictly defined value whereas the distance between bodies (particle) is an approximate value, at best [START_REF] Leifer | The relativistic non-linear quantum dynamics from the CP (N -1) geometry[END_REF][START_REF] Leifer | Gauge Field of the Self-interacting Quantum Electron[END_REF][START_REF] Leifer | The Quantum State-Sependent Gauge Fields of Jacobi[END_REF][START_REF] Leifer | The Project of the Quantum Relativity[END_REF]. Thereby, all well known solid frames and clocks even with the corrections of special relativity should be replaced by the flexible and anholonomic quantum setup. Then Yang-Mills arguments about the spacetime coordinate dependence of the gauge unitary rotations should be reversed on the dependence of the spacetime structure on the gauge transformations of the flexible quantum setup. One needs to build "inverse representation" of the unitary transformations by the intrinsic dynamical spacetime transformations.

In order to build such DST one needs the general footing for gauge fields and for "matter fields". Only fundamental pure quantum degrees of freedom like spin, charge, hyper-charges, etc., obey this requirement. One may assume that they correspond some fundamental quantum motions in the manifold of the UQS's. Then "elementary particles" will be represented as a dynamical process keeping non-linear coherent superposition of these fundamental quantum motions. One should, however, distinct the "total quantum state" (cum location) as an analog of the spatial coordinates of the system of material points with their "orientation coordinates", and the "unlocated quantum state" of the quantum degrees of freedom (QDF's) as an analog of the "unlocated shape coordinates".

The spacetime and its transformations will be built "from inside" of the "elementary" particle due to the separation of the group L ↑ + from the G = SU(N) acting on the quantum state space of rays CP (N -1) by the diffeomorphic coset transformations

The motions of the quantum degrees of freedom (QDF's) under the unitary transformations comprises the manifold of the unlocated quantum states (UQS's). These "elementary" motions replace "elementary particles" of the Standard Model. Its soliton-like excitations then realized as known "elementary particles". The intrinsic "unitary field" acting without super-selection rule continuously splits the multiplete of the spin, charge, hypercharge, etc., into zones. QDF's acts as unified "chiral" field whose dynamics will be discussed properly.

The fundamental quantum degrees of freedom like spin, charge, hyper-charges, etc., are common for gauge and matter fields. These fundamental quantum motions take the place in the manifold of the UQS's which described by the rays of states |ψ >∈ C N of the "unitary spin" S : 2S + 1 = N . Physics requires to use in this background the local coordinates of UQS's and the state-dependent generators of the unitary group G = SU(N) [START_REF] Leifer | Superrelativity as an Element of the Final Theory[END_REF][START_REF] Leifer | Inertia as the "threshold of elasticity" of quantum states[END_REF][START_REF] Leifer | State-dependent dynamical variables in quantum theory[END_REF]. This nonlinear representation of the SU(N) group on the coset manifold G/H = SU(N)/S[U(1) × U(N -1)] = CP (N -1) is primary and this is independent on the spacetime manifold. The last one should be introduced in a special section of the fiber bundle over CP (N -1) [START_REF] Leifer | Superrelativity as an Element of the Final Theory[END_REF][START_REF] Leifer | Inertia as the "threshold of elasticity" of quantum states[END_REF][START_REF] Leifer | Underlying Field Structure of Matter[END_REF][START_REF] Leifer | Field-shell of the self-interacting quantum electron, Annales de la Fondation Louis de Broglie[END_REF][START_REF] Leifer | The relativistic non-linear quantum dynamics from the CP (N -1) geometry[END_REF][START_REF] Leifer | Gauge Field of the Self-interacting Quantum Electron[END_REF][START_REF] Leifer | The Quantum State-Sependent Gauge Fields of Jacobi[END_REF][START_REF] Leifer | The Project of the Quantum Relativity[END_REF]. The breakdown of the global SU(N) symmetry down to the isotropy subgroup

H |ψ> = U(1) × U(N -1) of the some quantum state |ψ > has natural geometric counterpart in CP (N -1). The coset manifold G/H |ψ> = SU(N)/S[U(1) × U(N -1)] = CP (N -1
) contains locally unitary transformations deforming "initial" quantum state |ψ >. This means that CP (N -1) contains physically distinguishable, "deformed" quantum states. Thereby the unitary transformations from G = SU(N) of the basis in the Hilbert space may be identified with the unitary state-dependent gauge field U(|ψ >) that may be represented by the N 2 -1 unitary generators as functions of the local projective coordinates (π 1 , ..., π N -1 ) [START_REF] Leifer | The relativistic non-linear quantum dynamics from the CP (N -1) geometry[END_REF]. This manifold resembles the "shape space" of the deformable body [START_REF] Littlejohn | Gauge fields in the separation of rotations and internal motions in the n-body problem[END_REF][START_REF] Leifer | The relativistic non-linear quantum dynamics from the CP (N -1) geometry[END_REF][START_REF] Leifer | Gauge Field of the Self-interacting Quantum Electron[END_REF][START_REF] Leifer | The Quantum State-Sependent Gauge Fields of Jacobi[END_REF][START_REF] Leifer | The Project of the Quantum Relativity[END_REF]. But now it is the manifold of the deformed physically distinguishable UQS's, i.e. the geometric, invariant counterpart of the quantum interaction or self-interaction. Then the classical acceleration is merely an "external" consequence of this complicated quantum dynamics in the some section of the frame fiber bundle over CP (N -1). The local dynamical variables (LDV's) are new essential elements of the new quantum dynamics [START_REF] Leifer | State-dependent dynamical variables in quantum theory[END_REF]. They should be expressed in terms of the local coordinates π k of UQS's. Thereby they will live in the geometry of CP (N -1) with the Fubini-Study metric tensor

G ik * = (1/κ)[(1 + |π s | 2 )δ ik -π i * π k ](1 + |π s | 2 ) -2 , (2.1)
where κ is holomorphic sectional curvature of the CP (N -1) [START_REF] Kobayashi | Foundations of Differential Geometry[END_REF]. The contra-variant metric tensor field

G ik * = κ(δ ik + π i π k * )(1 + |π s | 2 ), (2.2) is inverse to the G ik * thereby G ik * G i * q = δ q k . (2.
3)

The affine connection agrees with the Fubini-Study metric is as follows

Γ i mn = 1 2 G ip * ( ∂G mp * ∂π n + ∂G p * n ∂π m ) = - δ i m π n * + δ i n π m * 1 + |π s | 2 .
(2.4)

The curvature tensor of Riemann in holonomic basis is proportional to the constant section curvature since

R i klm * = κ 2 (δ i l G km * + δ i k G lm * ) (2.5
) [START_REF] Kobayashi | Foundations of Differential Geometry[END_REF]. The flexible quantum setup inherently connected with local projective coordinates will be built from so-called LDV's [START_REF] Leifer | State-dependent dynamical variables in quantum theory[END_REF]. These LDV's realize a non-linear representation of the unitary global SU(N) group in the Hilbert state space C N . Namely, N 2 -1 generators of G = SU(N) may be divided in accordance with the Cartan decomposition:

[B, B] ∈ H, [B, H] ∈ B, [B, B] ∈ H. The (N -1) 2 generators Φ i h ∂ ∂π i + c.c. ∈ H, 1 ≤ h ≤ (N -1) 2 (2.6)
of the isotropy group H = U(1) × U(N -1) of the ray (Cartan sub-algebra) and 2(N -1) generators

Φ i b ∂ ∂π i + c.c. ∈ B, 1 ≤ b ≤ 2(N -1) (2.7)
are the coset G/H = SU(N)/S[U(1) × U(N -1)] generators realizing the breakdown of the G = SU(N) symmetry. Notice, the partial derivatives are defined here as usual:

∂ ∂π i = 1 2 ( ∂ ∂ℜπ i -i ∂ ∂ℑπ i ) and ∂ ∂π * i = 1 2 ( ∂ ∂ℜπ i + i ∂ ∂ℑπ i ).
Here Φ i σ , 1 ≤ σ ≤ N 2 -1 are the coefficient functions of the generators of the non-linear SU(N) realization. They give the infinitesimal shift of the i-component of the generalized coherent state driven by the σ-component of the unitary field exp(iǫλ σ ) rotating by the generators of AlgSU(N) and they are defined as follows:

Φ i σ = lim ǫ→0 ǫ -1 [exp(iǫλ σ )] i m ψ m [exp(iǫλ σ )] j mψ m - ψ i ψ j = lim ǫ→0 ǫ -1 {π i (ǫλ σ ) -π i }, (2.8)
[11].

Quantum relativity

The principle of Quantum Relativity (QR) was initially called "super-relativity" [START_REF] Leifer | Superrelativity as an Element of the Final Theory[END_REF][START_REF] Leifer | Inertia as the "threshold of elasticity" of quantum states[END_REF]) assumes the invariance of physical properties of "quantum particles" i.e. their quantum numbers like mass, spin, charge, etc. Such invariance may be lurked, say, behind two amplitudes |Ψ 1 >, |Ψ 2 > in two different quantum setups S 1 and S 2 . The invariant content of these properties will be discussed here under the infinitesimal variation of the "flexible quantum setup" described by the amplitudes |Ψ(π, P ) > due to a small variation of the boson electromagnetic-like field P α (π) treated as the set of the scalar functions relative π i coordinates in CP (N -1). The DST dependence of P α (π) will be established after the separation of the shifts, boosts and rotations in the manifold of the SU(N) generators.

The mathematical formulation of the QR principle is based on the similarity of any physical systems ("setup", if somebody wants) which are built on the "elementary" particles. This similarity is obvious only on the level of the pure quantum degrees of freedom of quantum particles. Therefore, all "external" details of the "setup" should be discarded as non-essential and only the relations of components of the "unitary spin" like (π 1 = ψ 2 ψ 1 , ..., π N -1 = ψ N ψ 1 ) should be taken into account. These relations will be taken as the local projective coordinates in the complex projective Hilbert space CP (N -1). One may think about these coordinates as parameters of the "shape of quantum particle" in the spirit of the [START_REF] Littlejohn | Gauge fields in the separation of rotations and internal motions in the n-body problem[END_REF]. This "shape" is the unlocated quantum state (UQS) of the "unitary spin" S = N -1 2 . These coordinates are analog of an angle in the trigonometry that is the invariant characteristic of all similar triangles. Thereby, the coefficients functions Φ i α of the generators of SU(N) defined as the Lie derivative of the local projective coordinates π i under the infinitesimal unitary variation of the appropriate parameter ǫ in (2.8).

4 Separation of the Poincaré generators from the AlgSU (4) and the dynamical spacetime

The old problem of the accelerated charged particle is an acute challenge for QFT, high energy physics, and for the theory of elementary particles. There is an interesting attempt to solve this problem in the spirit of my concept of the deformation of UQS [START_REF] Penheiro | An Extended Dynamical Equation of Motion, Phase Dependency and Inertial Backreaction[END_REF]. Namely, the "backreaction of space" clearly close to the DST concept [START_REF] Leifer | Field-shell of the self-interacting quantum electron, Annales de la Fondation Louis de Broglie[END_REF][START_REF] Leifer | The relativistic non-linear quantum dynamics from the CP (N -1) geometry[END_REF][START_REF] Leifer | Gauge Field of the Self-interacting Quantum Electron[END_REF][START_REF] Leifer | The Quantum State-Sependent Gauge Fields of Jacobi[END_REF][START_REF] Leifer | Quantum relativity as the way towards reality[END_REF]. It worse while to say two words about so-called Quantum Potential [START_REF] Bohm | An Ontological Basis for the Quantum Theory[END_REF]. Since in the depth of the "elementary" particle there is no the ordinary "physical" spacetime and DST has state-dependent nature, the ordinary gradient of the momentum in respect of pseudo-Euclidian coordinates has no sense. But this concept is very prolific for the intermolecular interactions that nicely demonstrated in the Complex Mechanics of Yang and its applications [START_REF] Yang | Complex Mechanics[END_REF]. Furthermore, the complexification of the spacetime coordinates and momenta is the step in the correct direction with the reservation about the functional nature of these coordinates: they are functions in some gauge "sheet" in the Hilbert state space.

The metric of the DST is state-dependent that may be demonstrated directly by the calculations of the square of the speed velocity dS 2 dτ 2 of the geodesic distance in CP (3) [START_REF] Leifer | The Project of the Quantum Relativity[END_REF]. "Diffusion" of the mass-shell is evident here but the scale of such diffusion is unknown since the value of the sectional curvature κ included in G ik * is a free parameter up to now. It is closely connected with the non-separability of the inertial mass m from the acceleration d 2 x dt 2 in the Newton's expression for the force

dp dt = m d 2 x dt 2 = -∂V ∂x .
The speed of the momentum variation will be treat now as field equation with TWS solution instead of the equation for trajectory of the point-wise particle.

In the case of the extended quantum electron [START_REF] Leifer | Field-shell of the self-interacting quantum electron, Annales de la Fondation Louis de Broglie[END_REF] one deals with the dynamical reconstruction of the G = SU(4) symmetry of the UQS down to the H = S[U(1)×U(3)] of the unitary rotation of the whole CP (3) geodesics. This geodesic carriers unperturbed dynamics of the self-interacting "free" electron. This internal dynamics of the spin/charge degrees of freedom in CP (3) cannot be directly connected with spacetime since this is "unlocated". Its spacetime coordinates are absent. Furthermore, we deal not with the "events" as points of the Minkowski spacetime but with a dynamical process. There is an analogy with the MRI method [15] of the coordinate prescription for voxeles in the (field-of-view) FOV and the "inverse representation" of the UQS's motion in CP (N -1) by the field dynamics in the DST [START_REF] Leifer | The relativistic non-linear quantum dynamics from the CP (N -1) geometry[END_REF][START_REF] Leifer | Gauge Field of the Self-interacting Quantum Electron[END_REF][START_REF] Leifer | The Quantum State-Sependent Gauge Fields of Jacobi[END_REF].

The MRI coordinate introduction is based on the known dependence of the frequency shift on the distance in the gradient magnetic field. Then known field amplitude and frequency gives the distance according very simple formula δ -→ x = k∇B. In our case the spacetime distribution of the gauge field and total wave function are unknown and they should be found.

I will introduce the definition of the Poincaré generators in the local DST as the special linear combinations of the Lie derivatives of the local projective coordinates (π 1 , π 2 , π 3 ) in directions given by the Dirac matrices in the Weyl representation. This construction is most transparent for the fundamental fermion like the electron. More general case of higher dimension should be discussed elsewhere. For this aim I will use the following set of the Dirac matrices

γ t =      0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0      , γ 1 = -iσ 1 =      0 0 0 -1 0 0 -1 0 0 1 0 0 1 0 0 0      , γ 2 = -iσ 2 =      0 0 0 i 0 0 -i 0 0 -i 0 0 i 0 0 0      , γ 3 = -iσ 3 =      0 0 -1 0 0 0 0 1 1 0 0 0 0 -1 0 0      . (4.1)
Then the corresponding coefficients of the SU(4) generators will be calculated according to the equation

Φ i µ = lim ǫ→0 ǫ -1 [exp(iǫγ µ )] i m ψ m [exp(iǫγ µ )] j mψ m - ψ i ψ j = lim ǫ→0 ǫ -1 {π i (ǫγ µ ) -π i }, (4.2)
[11] that gives

Φ 1 0 (γ t ) = i(π 3 -π 1 π 2 ), Φ 2 0 (γ t ) = i(1 -(π 2 ) 2 ), Φ 3 0 (γ t ) = i(π 1 -π 2 π 3 ); Φ 1 1 (γ 1 ) = -i(π 2 -π 1 π 3 ), Φ 2 1 (γ 1 ) = -i(-π 1 -π 2 π 3 ), Φ 3 1 (γ 1 ) = -i(-1 -(π 3 ) 2 ); Φ 1 2 (γ 2 ) = -i(i(π 2 + π 1 π 3 )), Φ 2 2 (γ 2 ) = -i(i(π 1 + π 2 π 3 )), Φ 3 2 (γ 2 ) = -i(i(-1 + (π 3 ) 2 )); Φ 1 3 (γ 3 ) = -i(-π 3 -π 1 π 2 ), Φ 2 3 (γ 3 ) = -i(-1 -(π 2 ) 2 ), Φ 3 3 (γ 3 ) = -i(π 1 -π 2 π 3 ). (4.3)
Such choice of the vector fields lead to the "imaginary" basic in local DST which conserves 4D Eucledian geometry along geodesic in CP (3) for real four vectors (p 0 , p 1 , p 2 , p 3 ) and correspondingly 4D pseudo-Eucledian geometry for four vectors (ip 0 , p 1 , p 2 , p 3 ).

The complex DST "tangent vector" in µ direction defines the four complex shifts in DST that will be introduced as follows:

∂ ∂x µ = Φ i µ ∂ ∂π i (4.4)
for 0 ≤ µ ≤ 3. In fact one may define the similar "tangent vector" in α direction

∂ ∂x α = Φ i α ∂ ∂π i (4.5)
for 1 ≤ α ≤ 15 in the space R 15 of the adjoint representation of the SU(4). Thereby, the DST cannot be treated as the "space of events". It is rather 10-dimension subspace of the adjoint representation of the SU(4). The quantum operator of the energymomentum will be expressed as the shift operator

P µ = ih ∂ ∂x µ = i h L Φ i µ ∂ ∂π i . (4.6)
Now one may introduce six generators of the boosts and rotations started from the well known definitions in terms of Dirac matrices [START_REF] Feynman | The Theory of Fundamental Processes[END_REF].

B x = (i/2)γ t γ x = (i/2)      0 1 0 0 1 0 0 0 0 0 0 -1 0 0 -1 0      , B y = (i/2)γ t γ y = (i/2)      0 i 0 0 -i 0 0 0 0 0 0 -i 0 0 i 0      , B z = (i/2)γ t γ z = (i/2)      1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 1      , R x = (i/2)γ y γ z = (i/2)      0 i 0 0 i 0 0 0 0 0 0 i 0 0 i 0      , R y = (i/2)γ z γ x = (i/2)      0 -1 0 0 1 0 0 0 0 0 0 -1 0 0 1 0      , R z = (i/2)γ x γ y = (i/2)      i 0 0 0 0 -i 0 0 0 0 i 0 0 0 0 -i      . (4.7)
Using the modified definition (2.8) one may find the corresponding coefficient functions of the vector fields of the Lorentz generators for boosts

Φ i (B α ) = lim ǫ→0 ǫ -1 [exp(ǫB α )] i m ψ m [exp(ǫB α )] j mψ m - ψ i ψ j = lim ǫ→0 ǫ -1 {π i (ǫB α ) -π i }, (4.8)
Φ 1 (B x ) = 1 2 (1 -(π 1 ) 2 ), Φ 2 (B x ) = -1 2 (π 3 + π 1 π 2 ), Φ 3 (B x ) = -1 2 (π 2 + π 1 π 3 ), Φ 1 (B y ) = - i 2 (1 + (π 1 ) 2 ), Φ 2 (B y ) = - i 2 (π 3 + π 1 π 2 ), Φ 3 (B y ) = i 2 (π 2 -π 1 π 3 ), Φ 1 (B z ) = -π 1 , Φ 2 (B z ) = -π 2 , Φ 3 (B z ) = 0, (4.9)
and rotations

Φ i (R α ) = lim ǫ→0 ǫ -1 [exp(ǫR α )] i m ψ m [exp(ǫR α )] j mψ m - ψ i ψ j = lim ǫ→0 ǫ -1 {π i (ǫR α ) -π i }, (4.10)
Φ 1 (R x ) = i 2 (1 -(π 1 ) 2 ), Φ 2 (R x ) = i 2 (π 3 -π 1 π 2 ), Φ 3 (R x ) = i 2 (π 2 -π 1 π 3 ), Φ 1 (R y ) = 1 2 (1 + (π 1 ) 2 ), Φ 2 (R y ) = - 1 2 (π 3 -π 1 π 2 ), Φ 3 (R y ) = 1 2 (π 2 + π 1 π 3 ), Φ 1 (R z ) = -iπ 1 , Φ 2 (R z ) = 0, Φ 3 (R z ) = -iπ 3 , (4.11)
Thereby, the eight λ-matrices (λ 4 , λ 11 ), (λ 2 , λ 14 ), (λ 1 , λ 13 ), (λ 5 , λ 12 ) of the AlgSU(4) were involved in the definition of the shift vector fields. It is easy to see that additional diagonal matrices , (λ 3 ), (λ 8 ), (λ 15 ) must be involved into the boosts and rotations definitions whereas four λ-matrices (λ 6 , λ 7 ), (λ 9 , λ 10 ) mixing electron-positron states with opposite spins all together with the eight λ-matrices comprise of the full set of the fifteenth matrices of the AlgSU(4).

Then the three generators

B α = Φ i (B α ) ∂ ∂π i (4.12)
define the boosts and three generators

R α = Φ i (R α ) ∂ ∂π i . (4.13)
define the rotations. The commutators of these vector fields is as follows.

[P 0 , P 1 ] = (ξ

1 = 2(1 + (π 1 ) 2 , ξ 2 = -2(π 1 π 2 + π 3 ), ξ 3 = -2(π 1 π 3 + π 2 ), [P 0 , P 2 ] = (ξ 1 = 2i(1 + (π 1 ) 2 ), ξ 2 = 2i(π 1 + π 2 π 3 ), ξ 3 = 2i(π 1 π 3 -π 2 )), [P 0 , P 3 ] = (ξ 1 = -4π 1 , ξ 2 = -4π 2 , ξ 3 = 0), [P 3 , P 1 ] = (ξ 1 = 2(1 + (π 1 ) 2 ), ξ 2 = 2(π 1 π 2 -π 3 ), ξ 3 = 2(π 1 π 3 + π 2 )), [P 2 , P 1 ] = (ξ 1 = -4iπ 1 , ξ 2 = 0, ξ 3 = -4iπ 3 ), [P 3 , P 2 ] = (ξ 1 = 2i(1 -(π 1 ) 2 ), ξ 2 = 2i(-π 1 π 2 + π 3 ), ξ 3 = 2i(-π 1 π 3 + π 2 )), [B 1 , B 2 ] = (ξ 1 = -iπ 1 , ξ 2 = 0, ξ 3 = -iπ 3 ), [B 1 , B 3 ] = (ξ 1 = -(1 + (π 1 ) 2 )/2, ξ 2 = (π 3 -π 1 π 2 )/2, ξ 3 = -(π 1 π 3 + π 2 )/2), [B 3 , B 2 ] = (ξ 1 = -i(1 + (π 1 ) 2 )/2, ξ 2 = -i(π 3 -π 1 π 2 )/2, ξ 3 = -i(π 1 π 3 + π 2 )/2), [R 1 , R 2 ] = (ξ 1 = iπ 1 , ξ 2 = 0, ξ 3 = iπ 3 ), [R 3 , R 2 ] = (ξ 1 = i(1 -(π 1 ) 2 )/2, ξ 2 = i(π 3 -π 1 π 2 )/2, ξ 3 = i(-π 1 π 3 + π 2 )/2), [R 1 , R 3 ] = (ξ 1 = (1 + (π 1 ) 2 )/2, ξ 2 = (-π 3 + π 1 π 2 )/2, ξ 3 = (π 1 π 3 + π 2 )/2), [B 1 , R 1 ] = (ξ 1 = 0, ξ 2 = 0, ξ 3 = 0), [B 1 , R 2 ] = (ξ 1 = π 1 , ξ 2 = π 2 ), ξ 3 = 0, [B 1 , B 3 ] = (ξ 1 = -i(1 + (π 1 ) 2 )/2, ξ 2 = -i(π 3 + π 1 π 2 )/2, ξ 3 = i(-π 1 π 3 + π 2 )/2), [B 2 , R 1 ] = (ξ 1 = -π 1 , ξ 2 = -π 2 , ξ 3 = 0), [B 2 , R 2 ] = (ξ 1 = 0, ξ 2 = 0, ξ 3 = 0), [B 2 , R 3 ] = (ξ 1 = -(1 -(π 1 ) 2 )/2, ξ 2 = (π 3 + π 1 π 2 )/2, ξ 3 = (π 1 π 3 + π 2 )/2), [B 3 , R 1 ] = (ξ 1 = i(1 + (π 1 ) 2 )/2, ξ 2 = i(π 3 + π 1 π 2 )/2, ξ 3 = i(π 1 π 3 -π 2 )/2), [B 3 , R 2 ] = (ξ 1 = (1 -(π 1 ) 2 )/2, ξ 2 = -(π 3 + π 1 π 2 )/2, ξ 3 = -(π 1 π 3 + π 2 )/2), [B 3 , R 3 ] = (ξ 1 = 0, ξ 2 = 0, ξ 3 = 0), [P 0 , R 1 ] = (ξ 1 = 0, ξ 2 = 0, ξ 3 = 0), [P 0 , R 2 ] = (ξ 1 = 0, ξ 2 = 0, ξ 3 = 0), [P 0 , R 3 ] = (ξ 1 = 0, ξ 2 = 0, ξ 3 = 0), [P 0 , B 1 ] = (ξ 1 = i(-π 1 π 3 + π 2 ), ξ 2 = -i(π 3 π 2 + π 1 ), ξ 3 = -i(1 + (π 3 ) 2 ),
5 The Hilbert space of the total quantum states and its gauge "sheets" fibration

De Broglie-Schrödinger corpuscle-wave duality establishes the relation between the Newton-Euler-Hamilton ODE's and the Schrödinger-Dirac PDE wave equations. This relation corresponds to the statistic ensemble of quasi-classical particles. There is, however, more general type of the "corpuscle-wave duality" in the class of the quasilinear PDE's of the first order where the field of the velocities naturally connected with characteristic curves serving trajectories for "particles" of some medium. I propose the quasi-linear PDE whose characteristic correspond to the trajectory of a single quantum electron. Dynamics of UQS's in the base manifold CP (N -1) serves as the "master" rules for quantum motions. This stems from de Broglie idea of the periodicity of some process with the frequency ω = mc 2 h in the energy parcel [START_REF] De Broglie | Recherches sur la Théorie des Quanta[END_REF]. I formulate the follow-ing requirement: the projection of the trajectory of a single quantum particle onto CP (N -1) should be a geodesic since all geodesics in CP (N -1) are closed that provide the periodicity by the natural manner. This condition formulates the gauge restriction on the divergency of energy-momentum field functions in DST.

The relativistic Hamiltonian vector field

H = c[P µ Φ i µ + K α Φ i (B α ) + M α Φ i (R α )] ∂ ∂π i + c.c. (5.1)
will be used for the eigen-value problem in terms of the PDE for the total wave function. Then the speed of the UQS components should be satisfied the following equation of characteristics

dπ i dτ = c h[P µ Φ i µ + K α Φ i (B α ) + M α Φ i (R α )] (5.2)
where τ is the quantum elapsed time counted from the start of the entanglement process. The Hamiltonian vector field leads to the quasi-linear PDE "Schrödinger equation"

ih dΨ(π, q, p) dτ = cP α Φ i α ∂Ψ(π, q, p) ∂π i + c.c. = E[Ψ(π, q, p)]Ψ(π, q, p), (5.3)
where the coordinates (p, q) correspond to the shifts, rotations, boosts and gauge parameters of the local DST, and E[Ψ(π, q, p)] is a functional of the total quantum state. One should remember that the normal vector to the solution Ψ(π, q, p) N = ( ∂Ψ(π, q, p) ∂π 1 , ∂Ψ(π, q, p) ∂π 2 , ∂Ψ(π, q, p) ∂π 3 , -1) (5.4)

and the tangent vector

T = (cP α Φ 1 α , cP α Φ 2 α , cP α Φ 3 α , ih dΨ(π, q, p) dτ ) = (cP α Φ 1 α , cP α Φ 2 α , cP α Φ 3 α , EΨ(π, q, p)), (5.5)
so that the "Schrödinger equation" may be written as the scalar product ( N T ) = 0, belong to some infinite dimensional functional space like the space of the complex value analytical functions.

In order to find physically acceptable solutions of this equation one needs to put the gauge and the "border" restrictions on meanwhile undefined functions P α . Our + ∂M α ∂ω α + M α ( ∂Φ(R i α ) ∂π i + Γ i il Φ(R l α )) = 0.

(5.10) with more complicated but similar TWS solutions. Nevertheless since each such solution contains the π i coordinates only in the rational manner the PDE's for the parallel transport condition (5.6) will be pure algebraic. Therefore, one has the field of the energy-momentum in the local 10D DST as the functions of π i on the each physical gauge "sheet" defined by the "border" choice of the integration constants.

It is important that DST argument of the TWS function ξ = 1 h q a C a , (1 ≤ a ≤ 10) will be equal to the action invariant of the single classical material point S = -a µ P µ + 1 2 Ω µν M µν = const (5.11) under the appropriate choice of these constants. Nevertheless, the solution of the quasi-linear PDE (5.3) is still open.

The DST manifold has only external structure, i.e. only embedding makes the sense for distance in this manifold. I would like to subscribe that this method of coordinatization of DST is in fact the first example outside of general relativity where measurable distance is the function of the energy-momentum.

Conclusion

I think we should come to term with following facts: 1) A "body" or even "elementary" quantum particle cannot be used as primordial elements of the consistent quantum theory. I proposed to use the unlocated quantum state (UQS) as the objective "beable" element of the quantum theory.

2) Our Universe is the functional manifold of quantum amplitudes (like Hilbert space) and the spacetime of our experience is merely some finite dimension gauge "sheet" of this manifold. Each "elementary" particle like electron is the superposition of the total quantum states of all Universe in each given spacetime point of the chosen "sheet".

3) The general rules of the quantum motion hidden in SU(N) group and its submanifold CP (N -1). It means that the reason of the quantum motion i.e. the existence of the quantum state is the coset action of the unitary field.

Quantum Relativity is a new kind of the gauge theory: instead of the adaptation of unitary transformations to spacetime location one needs to accommodate dynamical spacetime structure to the unitary field acting in the space of the UQS's. This gauge theory is state-dependent with variable spacetime structure that should be properly studied.

requirement tells that the projection of the trajectory of a single quantum particle onto CP (N -1) should be a geodesic. Hence, the covariant derivative in the sense of the Fubini-Study metric of the velocity of UQS dπ i dτ should be zero

(5.6)

One sees that the dynamical system for non-linear field momentum is self-consistent since the speed of the traversing the geodesic in CP (N -1) is not a constant but a variable value "modulated" by the field coefficients P α . Let me take initially only the shifts in DST without rotations and boosts. Then in the equation (5.6) one will have the summation only of four terms

(5.7)

In order to get the field equations in DST I use the definition of the DST derivative. Thus one may rewrite this equations for k = i as follows

Thus one has the gauge restriction in the form of the field equation. For the parallel transported Φ i µ this gauge restriction coincides with the ordinary Lorentz gauge. This linear PDE has the traveling wave solutions (TWS), say, in the form

(5.9)

Such solutions realize the state-dependent gauge conditions on the energy-momentum (potentials) and show that in the given definition of the DST coordinates x µ the complicated highly nonlinear field equations (5.7) transform into the linear PDE's (5.8) with soliton-like solution (5.9) or within more wide class of TWS's.

In general case of the full Poincaré motions in 10D DST one has correspondingly