Subgroups of the group of generalized Lorentz transformations and their geometric invariants

DOI10.3842/SIGMA.2005.017zbMath1094.83001arXivmath-ph/0511077MaRDI QIDQ2495131

Publication date: 4 July 2006

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/math-ph/0511077

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zbMATH Keywords

spontaneous symmetry breaking Finslerian space-time Lorentz, Poincaré and gauge invariance

Mathematics Subject Classification ID

Symmetry breaking in quantum theory (81R40) Special relativity (83A05) Applications of local differential geometry to the sciences (53B50) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40)

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