Spin as Dynamic Variable or Why Parity is Broken

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1 Sin as Dynamic Variable or Why Parity is Broken G. N. Golub There suggested a modification of the Dirac electron theory, eliminating its mathematical incomleteness. The modified Dirac electron, called dual, is described by two waves, one of which is the Dirac wave and the second dynamically restores the symmetry unused in the Dirac theory of the Dirac euation. There has been roduced a set of the conserved currents which are generated by euations of the dual electron. It is shown that, although, it consists of the vector, axial and left currents, nevertheless, it has mirror symmetry. It is also shown that if the observed electron follows the dual electron euations it would violate the mirror symmetry. The results of the aer for the first time exlain the ways and the reasons of mirror symmetry being created and broken in the nature. PACS: Pm, Ly 1. Introdaction Dirac wave euation [1-4] i mx 0 (1) has been intended for the electron descrition with the sin, co-oerating electromagnetic forces. A vector conserved current J x x x, (2) generated by this euation, at inclusion of electromagnetic interaction becomes an electromagnetic current of an electron. On the basis of Dirac euation and Maxwell euations within uantum electrodynamics almost comlete descrition of electromagnetic roerties of an observable electron is reached. But for the descrition of weak interactions in which the observable electron articiates, it is necessary to use the currents which conservation is not generated by Dirac euation (1). In Standard model of electroweak interactions[5-8], in which the descrition of weak interactions of an observable electron is reached, the satial structure of its weak currents should be taken from exerience. As weak interactions break mirror symmetry, it is reresented imossible, that based on secularly symmetric euation (1) the Dirac theory of an electron could generate weak interacting currents of an electron. But what is reresented imossible from one oint of view, can aear ossible from some other oint of view. To come to such other oint of view it is necessary to distinguish, first, Dirac wave euation and the Dirac s theory of an electron based on it. The last includes, besides the wave euation, two more sinor euations, algebra of the Dirac - matrixes and the geometrical theory of Dirac bisinor generated by them. Wave euation (1) really it is not caable to generate the left remaining current. But in the Dirac theory of an electron there can be enough lace and ossibilities to generate not only vector conserved currents. Secondly, hysical interretation of the Dirac theory a icture of a Dirac electron extremely strongly limits the use of the mathematical formalism, actually hiding its true ossibilities. The icture of a Dirac electron "is ground" for the descrition of an electromagnetic electron and it aears incomatible with attemt to describe an - 1 -

2 electroweak electron, using a mathematical formalism of the Dirac theory. If we set such urose, existing interretation should be modified. Originally to modification should be subject, on - to a being, only one, but key concet of the Dirac theory electron sin. As a result of modification of sin should turn from the nomenclature size only indirectly influencing dynamic rocesses, into the real dynamic variable, same, as an electron imulse. The initial mathematical structure of the Dirac theory remains thus without changes only sense and roles of the euations will change. As a result it will become clear that violation of arity which we observe in the nature, contains in the hidden look - in the Dirac theory of an electron. In it some "secret" side of the euation of Dirak also consists. Sense of the real work is in its disclosure. 2. The Dirac sinor euation Unlike other fundamental euations of hysics using language of the analysis and geometry, Dirac euation uses analysis and algebra language.. Because of this, in the Dirac's theory aear two of the Dirac euations: one is differential or wave, the other algebraic or sinor. The latter is usually called the Dirac euation in the imulse reresentation. Having substituted in the wave euation (1) the decision for a lane wave with both signs of freuencies x e ix U, (3) let's receive the Dirac sinor euation: m U. (4) Here U - Dirac bisinor, euation looks like: Dirac sinor current j 0 and m imulse and mass of an electron. The interfaced U m 0. (5) is defined by exression j U U (6) also satisfies to a condition received by a standard method from (4) and (5): j. (7) 0 Also from Dirac sinor euation and the interfaced euation it is ossible to receive ratio U U U U, (8) m from which we will receive normalization of bisinors U U (9) and exression of a free sinor current in four-dimensional seed of an electron v m v U U. (10) Above we followed a usual and most common way of creation of the Dirac theory[4, 9 11], consisting that Dirac sinor euation is deduced from the wave euation (1). Meets as well an alternative way at which start with the sinor euations and then ass to the wave[3, 12]. In the real work we will follow an alternative way of creation of the theory, though have begun with the usual. So, we will accet that the initial euation of the Dirac theory is Dirac sinor euation (4). To deduce from it Dirac wave euation, we should, oerating formally, to make

3 , i U x (11) and to receive as a result of lane wave Dirac euation. Then, using a suerosition rincile [3], to receive the wave euation (1). But for us it is imortant that at the carriedout relacement a sinor current (6) asses in lane wave current j J x x x (12) l and euality (7) asses to the law of reservation of lane wave current l x 0. J (13) Therefore we will call euality (7) law of conservation of a sinor current. Now we aroach to central oint of our consideration of the Dirac theory. It consists that Dirac sinor euation short defines a bisinor, leaving uncertain a half its comonent. In a icture of a Dirac electron it has a natural exlanation: an electron has a sin which behaviour is not defined neither wave, nor sinor by Dirac euations. What does it mean in sense of use of degrees of freedom available for a Dirac electron? It means, simly saying that in dynamic sense the Dirac electron is half emty. In itself it would not cause any uestions if the observable electron co-oerated only electromagnrtically and as it would well be described by a Dirac electron as it occurs now. But the observable electron, excet electromagnetic, co-oerates with weak forces, for what the existing Dirac electron is not caable. (Here, to a ossible uestion of the reader: Doesn t the Standard model of electroweak interactions describes all interactions of a Dirac electron, both electromagnetic, and weak? it is necessary to answer: No, it does not describe. The Standard model is a modification of the Dirac theory, it describes the modified Dirac electron and it ossesses all interactions of an observable electron. ) It is comarable now with dynamic incomleteness of a Dirac electron and dynamic "overoulation" in comarison with Dirac of an observable electron. There is a uestion: Are they connected with each other, i.e. is incomleteness of a Dirac electron the reason of weak forcesat it? It is ossible that it is so, and then it is necessary to try to comlete the Dirac theory of an electromagnetic electron to the comlete dynamic theory in hoe to receive an electroweak Dirac electron. Another art of this work is devoted to attemt of imlementation of this hoe. The first that it is necessary to make for this urose to find the second sinor euation which together with Dirac sinor euation will make full system of the euations for a Dirac bisinor. 3. The euation of own olarisation It, of course, should be the euation of sinor olarisation. Usually [4] bisinor olarisation is described by a four-dimensional vector of olarisation which, by definition, is eual in system of rest of a bisinor to a three-dimensional vector of sin to which in this system the tensor of a bisinor sin, in turn, is reduced. Also it is usual to call a vector of olarisation a sin vector. Though it is not absolutely correct, as sin as the angular moment is a tensor, but it is convenient and we will use also this name. The reason of its common use is that within a icture of a Dirac electron it is imossible to establish true sense of a vector of olarisation. This sense makes a theoretical riddle of the Dirac theory, to solve which it is ossible only by its modification. Let's call a vector of own olarisation of a bisinor U, s vector U - 3 -

4 Here, 5 A s U, s U, s. (14) i. From Dirac sinor euation follows the euity A U, s U, s 0. (15) Using it after multilication of the euation of Dirac at the left on 5 From here comes and from consideration s in system of rest follows out the euation A su, s U, s. By multilying it at the left by U, s 5 U, s, we will receive s 0. (16), s 0, (17) A, let's receive ss. 2 s euation of own olarisation of a Dirac bisinor looks like: and the interfaced euation view U, s s The euations of a dual bisinor Therefore, it should be carried and, it means,. Thus, A s U, s 0, (18) A Let's write out the received full system of the euations with which should satisfy a Dirac bisinor mu, s 0. (19) A s U, s 0 These are the last euations in our work, belonging to the existing Dirac theory, having a habitual aearance and interetiruyemy within a icture of a Dirac electron. We will begin modification of the Dirac theory with release of this system from influence of a icture of a Dirac electron. For this urose, first, we will divide the first euation on m. Secondly, we will get rid of concet of a freuency sign, having relaced with this concet with a bisinor sign. Dirac bisinor, thus, can be ositive and negative. Thirdly, we will enter designation V. Fourthly, we will relace designation of a vector of olarisation: a s. As a result we will receive the following system of euations: V v U v a a U v a, 0. A, 0 To these euations it is necessary to add received before definition v and a : v Uv, a VUv, a. (21) a Uv, a AU v, a Systems of the euations (20) and (21), as it is obvious, ossess symmetry of the to and bottom euations. Let's call this symmetry dual. In the existing Dirac theory this symmetry is ignored and collases, aarently already from system (19). The urose of our modification is to kee this symmetry and to take it as a rincile definition of all (20) - 4 -

5 mathematical and hysical concets of the modified theory. The source of dual symmetry Dirac algebra, in it dual symmetry is exressed by symmetry of forming systems: V, V 2g. (22) A, A 2g Let's begin necessary definitions with system (21). According to the Dirac theory a v - fourdimensional seed of an electron, is its olarisation. According to dual symmetry so cannot be or both of them are seeds, or they are olarisation. Actually, aarently, both of them and that, and another in relation to a bisinor they are olarisation, in relation to an electron seeds. For their distinction we will enter at first the general definition for vectors in Minkowsky saces of various hysical dimensions (imulses, olyarizatsiya, etc.), excet the most co-ordinate sace time Minkowsky. Let's call vector external, if. Let's call vector d internal, if At last, let's call vector boundary, if cc 0. These definitions relace terms time-like, sacelike and lightlike, resectively, exressing domination of habitual sace time. Now we will call v in the external seed of, and, resectively, a - in the bb 0 dd 0. v, a an electron and external olarisation of a bisinor internal seed of an electron and internal olarisation of a bisinor. Let's ass to system (20). Having increased its euations on m, let's receive the following system of euations: V mw, 0. (23) A mw, 0 Here dual symmetry comels us to accet the following definitions. Vector call an external imulse of an electron, a vector electron, a bisinor W, U b c mv let's ma let's call an internal imulse of an let's call dual. System (23) there is a system of the euations of a dual bisinor. Let's write out searately the euations for ositive and negative dual bisinor: V V m W, 0 m W, 0. (24) A m W, 0 A m W, 0 Aarently from these euations, for transition from ositive bisinor to negative it is necessary to change a weight sign. Therefore further we will study only ositive bisinor, W W,. As it will be visible from further, all received having entered designation results of work are transferred from ositive bisinor on negative without changes. Let's write finally initial euations for a ositive bisinor and its interfaced: W V m 0 V m W 0. W 0 A m W 0 A m 5. Conserved currents of a dual bisinor Let's comare number of degrees of freedom of Dirac and dual bisinor. Their geometrical number is identical and eual to five: three external lus three internal minus communication (16). But at a dual bisinor all are dynamic five, at Dirac only three. As a result of a Dirac bisinor has one remaining current, dual as we will see, six. (25) - 5 -

6 We now define the meaning of a dual sinor current. This current deends on two dual bisinors - initial W and defined by: Here, the index M, 1 1 R 2 V A L 2 V A and final W, which is the solution of the conjugated system, - j W W. (26) M M takes values V, A, R, L, and also there introduced the notations:. Thus, one air of the dual bisinors generates four different currents differentiated by the sace-time structure, only two of which are linearly indeendent. The essential difference of the Dirac sinor current from the dual sinor current deends on the first two imulses - and, and the second deends on four -,,,. We now define the conservation laws for the dual sinor currents. As an examle, we resent two conservation laws, received by the standard methods from the system(25): jv 0. (27) ja 0 The difference between the initial and final imulses which deends on the sinor current will be defined the current imact. Then, the first law of conservation out of (27), which is similar to a single conservation law of the Dirac sinor current, claims that the vector current is orthogonal to its external imact. Similarly, the second law states that the axial current is orthogonal to its internal imact. The law of conservation deends on the orthogonal nature of the sinor current and its imact. We now define two scalar values for dual bisinors a true scalar S W W and seudoscalar P W 5W, which, as well as the currents, deends on four imulses. If the current is not orthogonal to its imacts, and their roduction is roortional to either S, or P, in this case we define this euation as a nonconservation law. Although, the sinor currents have no aarent dual structure, their laws of conservation / non-conservation have a clear dual structure defined by the current imact. It is convenient to reresent the dual structure of conservation/ non-conservation laws in the form of 2 2 matrix, with the external and internal laws located on its diagonal, and its antidiagonal having the raising laws, the imact of, and the lowering ones, with exosure to. We roceed to finding all of the conservation laws for dual sinor currents. If we assume the euation system (25) indeendent, i.e., written for two different Dirac bisinors, these euations will generate two indeendent conserved Dirac currents - external and internal, and a set of conservation laws (27) for such a system will be comlete. Though, the set of diagonal laws(27) may not be comlete for the dual bisinor. The dual bisinor euations can generate such relations between currents and imact that under certain conditions some non-conservation laws can become conservation laws. We call such conservation laws conditional, unlike unconditional laws (27). Our roblem now touches the uestion whether the dual bisinor generates conditional conservation laws and what their structure is. To solve this uestion, we write all the roducts of the imulses and currents resulting from the system (25): jv jv ms jv jv mp. (28) ja ja mp ja ja ms Using these relations, we find that all the laws of conservation / non-conservation are generated by the system (2). We write the result in the form of matrices with the dual

7 structure where each cell contains two euations. There reresented two of such matrices; one we will collect all the scalar euations or contains S and the second - all the seudoscalar or contains P. Besides, to ensure symmetry, including the mirror one, we add similar euations to these matrices, which have the sums of imulses instead of the imacts. The scalar matrix of such euations resented as follows: jv 0 jr ms jv 2mS jl ms. (29) jr ms ja 0 jl ms ja 2mS There are two conservation laws and two non-conservation laws in it alicable for the right antidiagonal currents. The seudoscalar matrix resented as follows: ja 0 jr mp ja 2mP jl mp. jr mp jv 0 jl mp jv 2mP It contains four non-conservation laws. As it can be seen from the structure of matrices obtained, the dual structure was related to the sace-time structure - there are the vector and axial currents on the diagonal and on the antidiagonal - there are only the chiral ones. Now we need to determine whether there are the conditions, the imlementation of which will transform the laws of non-conservation in the conservation laws. Such conditions are not difficult to find. They are contained in the diagonal euations of the two matrices. It is necessary to comare the uer diagonal euations of the scalar matrix to the lower diagonal euations of the seudoscalar matrix. The result is the same in the reverse comarison. Firstly, we comare the euations with the sums of imulses. They imly that the scalar S is eual to zero if the sums of external and internal imulses haen to be roortional. The conseuence of this will be conservation the of the right antidiagonal current. Nevertheless, we have to check whether the found condition correlates with the mirror symmetry. We will write down the condition for zero imulse comonents:. To ensure the mirror symmetry, the factor must take both ositive and negative values and all the uantity of the imulses, corresonding with the condition, and must contain both ositive and negative values of zero comonents of the external and internal imulses. Thus, it is imossible as the system (25) has a solution only with the ositive energies. Therein, the condition can not be found, i.e. destroys the mirror symmetry, and hence, the system (25) can not conserve the right current. We now comare the euations to the imacts. They imly that the seudoscalar P becomes zero if the external and internal imacts are roortional. The conseuence of this is the emergence of the four conserved currents: two left antidiagonal and two diagonal. This means that the external euation begins to conserve the internal current and the internal euation conserves the external current, or what is the same, the left and right diagonal currents begin to conserve searately. Since the energy of the external imact as well as of the internal can have any signs, the found condition exoses mirror symmetry. Thus, in our study we have answered the uestion above the dual bisinor generates four conventional conservation laws: two antidiagonal and two diagonal. (30)

8 6. A dual electron Now we consider the transition from a system of the sinor euations (25) to the corresonding system of the wave euations. Therefore, we use the rule (11). The first euation of the system(25) becomes the Dirac euation, which, in terms of the dual structure, naturally called the euation of external electron wave. We denote this wave as, where the coordinates of the external configuration sace are denoted through. x The second euation becomes the euation of internal electron wave, which we denote by, where the coordinates of the internal configuration sace are denoted through. x As a result of both transitions, the following system of the wave euations is to occur: iv m x 0. (31) i m x 0 A The hysical system rovided by these wave euations is denoted as the dual electron. Thus, the last, described by two waves, kinematically and inextricably linked with each other, as generated by the same dual bisinor W. It is, therefore, natural to introduce the dual wave comosed of inner and outer dual electron waves on the basis of the concet of the dual isosinor comosed of two dual bisinors: x. (32) x Now we state that the dual electron described by the dual wave and the Dirac wave is art of a dual wave. On comaring of (25) and (31), we see that the system (31) gives the wave exression of the dual symmetry, which is contained in the sinor form of the system (25), on the other hand, the system(25) reresents a euation of the dual electron in the imulse reresentation. 7. Conserved currents of the dual electron Let s consider the structure of the wave currents of the dual electron. Transition from the dual sinor currents to the dual wave currents is roduced by the rule(11) and leads to the situation when the wave currents obtain exlicit dual structure defined by the wave functions. This structure is naturally combined with the dual structure of the matrices (29) and(30), which, in turn, corresonds to the comonents of the dual isosinor. The diagonal wave currents describe transitions without changing the wave, i.e., corresond to the movements - external and internal, and the antidiagonal currents change the tye of wave and corresond to the conversion rocesses. All the conclusions on the unconditioned and conditioned conservation laws of the sinor currents are transferred to a lane-wave currents unchanged. We write the remaining six conditionally conserved or resonance lane-wave currents in the form of the following matrix, using the notation j r, j l : r l l J. (33) l r l Here the indices,,,, mark external, internal, raising and lowering currents resectively. From the form of this matrix it follows that the basis of the conserved currents structure of the dual electron is the algebra Li generators of the grou U SU, acting in the dual isosin sace (32) R R L x x L

9 8. Parity violation by a dual electron Let us finally turn to the issue of mirror symmetry and its violation by the dual electron. In comarison to what we have it clearly violates mirror symmetry matrix of the currents (33) - and then, taking in consideration the oint where we started an obvious mirror symmetric system of euations (25) - we see the aradoxical contradiction reuiring its solution. The root of this contradiction contains in the matrices (29) and (30), so we leave matrix currents (33) for some time and introduce the following definitions. A reflection of three satial coordinates will be called P- reflection and the symmetry about it called P- symmetry. A system of mathematical euations will be defined as the theoretical P- symmetry, if P-reflection goes into itself in this case. The hysical henomenon under observation called having an exerimental P-symmetry, if the P-reflection turns into the same hysical henomenon observed. Let us now consider the matrices (29) and(30), aying attention only to the conversion currents and considering the chiral and resonance condition:. As for them, it is stated that only left conversion currents conserved. While making P-reflection, we see that the uer conversion euations ass into the lower and lower - into the uer. As a result, after the P-reflection, we get the same system of euations, and the same left conserved current. Conseuently, the matrices (29) and (30), and the system of euations (25) have a theoretical P-symmetry. As it is easy to see that the system with the left conserved currents is P-symmetric because under the P-reflection when the left current goes into the right, it loses its conservation and the right, going into the left, it acuires. Thus, P- reflection changes both chirality and conservation, and as a result, they are inextricably linked to each other the left current is always conserved and the right - never. The essence of this aradox is that the only difference between the external and internal imulses generates an imact and, thus, the law of conservation so that the sum of imulses of the conservation law does not. If we imagine that the observed electron is described by euations of the dual electron, then, having the theoretical P-symmetry, it will disrut the exerimental P- symmetry. At the same time we must imly a rule, as we have done before, that exists in nature and resuoses that only conserved currents can be observed. Then, the observed dual electron with the exerimental P-symmetry and the P-reflection, the left observed current is exected to ass into the right one, and therefore, into the conserved current, which is imossible. The cause for differences of theoretical and exerimental P-symmetries of the dual electron is considered to be the discharge of the observed currents from P- symmetric mathematical structure that occurs in violation of the P-symmetry. Returning to the current matrix (33), we should say that it causes only the aearance of contradiction. This haens as a result of reresentation of only one art of a comlete attern given by matrix (30), and the one that indicates only the observed currents and, thereby, exhibits exerimental violation of mirror symmetry. The right, non-conserved currents, roviding theoretical mirror symmetry, can not be reresented in the matrix(33), so this symmetry is hidden. Thus, we found the dual electron consistent but aradoxical - having mirror symmetry theory, the electron breaks it exerimentally. 9. Internal wave P Having solved the second of the euations (31), let's receive a lane internal wave of a dual electron in a view

10 ix x e W. (34) Let's find out hysical sense of a wave vector of this wave. Its definition as internal imulse ma gives nothing, as sense of a vector of olarisation a in the existing theory is unknown. An exit in this situation is use of dual symmetry. We know the sense of a wave vector of an external wave is a vector of energy imulse of an electron. To transfer this sense on an internal wave vector, it is necessary to make such definition of this concet which would be dual invariant. For this urose we should roceed in this definition not from relativistic mechanics of our outside world, and from a structure of the wave. Let's make such definition: the wave vector of a wave is a vector of energy imulse of that article which is described by a wave; energy is that art of a wave vector which remains in rest; an imulse is that art of a wave vector which in rest disaears. Having alied this definition to an external wave, we will receive Let's aly it now to internal wave: E,. (35), E. (36) Such is a conseuence of dual symmetry: internal energy of a dual electron is a threedimensional vector, and an internal imulse a scalar. From a ratio (16) E E 0, (37) from where we receive E. (38) E The internal imulse is comletely defined by external movement and internal energy. Internal movement is not indeendent from external: internal energy - is the external energy redistributed in the anisotroic image. At external rest there can t be internal movement. 10. Internal time and sace Let's find out now sense of internal configuration sace, using the method alied above. Let's make such wave definition of time and sace: time is that co-ordinate of configuration sace which in a hase of the lane wave extending in this sace, is increased by energy; sace is that co-ordinate which is increased by an imulse. Let's aly this definition to an external wave: x t, r. (39) Now we will aly it to an internal wave: x r, t. (40) Internal time of a dual electron aears three-dimensional, and internal sace - onedimensional. The dual lane wave describing a free dual electron, looks like: i Et x r e W. (41) i r x Et e W Acceted as it is reresented, interretation of internal time can be received if to start with its wave nature. The structure of a lane internal wave allows to assume that tridimentionality of internal time has otential sense, defining the ossible directions of its

11 current, actually it has one direction which is set by a vector of internal energy. Let's coy exression for a lane wave, having allocated in it weight of electron: imvx im e W e W. (42) imax im e W e W From this it follows that lane waves of a dual electron reresent two fluctuations with own freuency m and own times and. It is imortant that the role of arrows of own times for these fluctuations is layed by seeds v and a, being olarizations (21) of dual bisinor Therefore dual bisinor W comletely defines a structure of a lane dual wave and is for it a bisinor of own times. Thus, we come to the general conclusion that in the theory of a dual electron the role of Minkowsky sace time should be changed in comarison with the theory of a Dirac electron. This change as it is obvious, mentions only hysical sense of co-ordinates in Minkowsky sace, without concerning its mathematical structure. Aarently, it is simlest to make this modification, having entered concet of Minkowsky variety. It is necessary to understand the mathematical four-dimensional seudo-euclidean sace which co-ordinates in itself have no hysical sense as they are. The hysical sense at co-ordinates of Minkowsky variety arises only when the bisinor wave extends in it and this sense is defined by this wave. For an external wave the Minkowsky variety is meaningful (39), for an internal wave (40). Now we can eliminate an index in designation of configuration sace and enter such definition of a lane dual wave on variety Minkovsky x : x. l x (43) x It is necessary to mention that it is necessary to make reflexion of satial axes for ensuring mirror symmetry according to their hysical sense. Then, as well as it is necessary, the external wave will extend in vector sace, and internal in the seudo-vector. W. 11. Comarison to exerience In conclusion, we should say that we have almost reached the goal - the satial structure of conserved currents of the dual electron coincides with the structure of the interacting currents of the observed electron, excet for the weak neutral current, which is observed in the electron that is not comletely axial. Therein, this difference is robably aarent. Let us comare, for examle, the structures of the currents in Møller scattering of two dual electrons and two observed electrons described by the Standard Model. The dual electron current must have the left current including the electrodynamic vector current and axial current. Without going into the roblem of the dual wave charges we can assume that it should effectively be neutral. In this case, the neutral non-vector current dual electron will consist of the axial and left currents and its structure can be uite consistent with that of the 2 observed electron at the value of the Weinberg angle sin 1 W 4. Moreover, the resence 0 of the left neutral current may exlain as to why the Weinberg angle is not eual to Discussion In the real work the origin of remaining currents in the Dirac theory is studied. In work it is shown that if in the Dirac theory to start with sinor geometry and its simmetry, other structure of conserved currents, than in the icture of a Dirac electron based on the wave euation turns out. These differences are the following: α) six currents remain;

12 β) arity is broken; γ) the structure of currents is close to observed at a hysical electron. The consideration carried out in work reresents immanent modification of the Dirac theory, i.e. such one, which, without changing the initial euations of the theory, gives them new senses, develoing existing in the theory of symmetry is so far, as far as it is ossible. Work has heuristic character and its results reresent only the first contours of a new icture of a dual electron which in the comlete develoment should include a icture of a Dirac electron and, thereby, relace it. The similarity of satial structures of currents of a dual electron and electron of Standard model is combined with a dissimilarity of their hysical senses. The uniue ossibility to ull them together as it seems now is the assumtion of existence at of dual structure in neutrino. As mostly remaining currents of a dual electron are conditional, transition to a co-oerating dual electron reresents, aarently, yet not contemlated roblem. 13. Conclusion We conclude the article commenting on the comarison of the dual electron and the electron of the Standard model. The dual electron is a mathematical construct, generated by the Dirac algebra and existing indeendently of exerience. The electron of the Standard model is essentially taken from exerience. If their roximity would not be accidental, it would mean that the world is ruled by algebra. References [1] P. A. M. Dirac, Proc. Roy. Soc. (London) A117, 610 (1928); A118, 351 (1928). [2] P. A. M. Dirac, The Princiles of Quantum Mechanics (Clarendon Press, Oxford, 1958). [3] R. P. Feynman, The Theory of Fundamental Processes (Benjamin, New York, 1961). [4] J. D. Bjorken, S. D. Drell Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964). [5] S. L. Glashow, Nucl. Phys., v. 22,. 579, [6] S. Weinberg, Phys. Rev. Lett., v. 19,. 1264, [7] A. Salam, In: Elementary Particle Theory / Ed. N. Svartholm (Aluist and Wiksell, Stockholm, 1968), [8] L. B. Okun, Letons and Quarks (North-Holland, Amsterdam, 1982). [9] F. Halzen, A. D. Martin, Quarks and Letons (John Willey & Sons, New York, 1984). [10] S. S. Schweber, An Introdaction to Relativistic Quantum Field Theory (Row, Peterson and Comany, New York, 1961). [11] C. Itzykson, J. B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980). [12] V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics (Pergamon Press, Oxford, 1982)