A special-relativistic theory of the locally anisotropic space-time

Abstract. We study the geometric phase transitions that accompany the dynamic rearrangement of vacuum under spontaneous violation of initial gauge symmetry. The rearrangement may give rise to condensates of three types, namely the scalar, axially symmetric, and entirely anisotropic condensates. The flat space-time keeps being the Minkowski space in the only case of scalar condensate. The anisotropic condensate having arisen, the respective anisotropy occurs also in space-time. In this case the space-time filled with axially symmetric condensate proves to be a flat relativistically invariant Finslerian space with partially broken 3D isotropy, while the space-time filled with entirely anisotropic condensate proves to be a flat relativistically invariant Finslerian space with entirely broken 3D isotropy. The two Finslerian space types are described briefly in the extended introduction to the work, while the original part of the latter is devoted to determining observable 3-velocities in the entirely anisotropic Finslerian event space. The main difficulties that are overcome in solving that problem arose from the nonstandard form of the light cone equation and from the necessity of correct introducing of a norm in the linear vector space of rapidities.

Section: The F Lat Relativistically-symmetric Finslerian Event Space mentioning

confidence: 99%

“…Against the background of the research made in terms of SME, the alternative (so called Finslerian) approach to the Lorentz symmetry violation (see, in particular, [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]) gets ever more popular. The latter is based on the Finslerian, rather than pseudo-Euclidean, geometric model of flat event space.…”

Section: Introductionmentioning

confidence: 99%

Rapidities and Observable 3-Velocities in the Flat Finslerian Event Space with Entirely Broken 3D Isotropy

Bogoslovsky¹

2008

“…Integration of equations (1) leads to the 1 It is worth noting that, irrespective of the problem of violation of Lorentz symmetry, in the literature consideration has already been given to the mechanism of the dynamical breaking of the initial gauge symmetry which is alternative to the standard one; instead of the elementary Higgs condensate there appears a scalar fermion-antifermion condensate [11]. 2 For more details see [7].…”

Section: The 4-parameter Subgroup Of Lorentz Group and Its 3-parametementioning

confidence: 99%

“…In contrast to such string-motivated theory (see also [5,6]) there exists another, Finslerian approach to the problem [7,8,9,10], which permits Lorentz symmetry violation without violation of relativistic symmetry. It is based on the following idea.…”

Section: Introductionmentioning

confidence: 99%

Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants

Bogoslovsky

2005

Abstract. It is shown that the group of generalized Lorentz transformations serves as relativistic symmetry group of a flat Finslerian event space. Being the generalization of Minkowski space, the Finslerian event space arises from the spontaneous breaking of initial gauge symmetry and from the formation of anisotropic fermion-antifermion condensate. The principle of generalized Lorentz invariance enables exact taking into account the influence of condensate on the dynamics of fundamental fields. In particular, the corresponding generalized Dirac equation turns out to be nonlinear. We have found two noncompact subgroups of the group of generalized Lorentz symmetry and their geometric invariants. These subgroups play a key role in constructing exact solutions of such equation.

“…Furthermore, proceeding with the suggestion of [18], we also construct versions of (1.1) that are simultaneously Lorentz violating and nonlinear: such equations have also not been studied before in general; however we note that one example of such an equation, without derivatives in the nonlinearity, has been studied in [24,25], motivated by anisotropic space-times [26].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dirac Equations

Parwani

2009

Abstract. We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.