Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 1 (2005), 017, 9 pages      math-ph/0511077      https://doi.org/10.3842/SIGMA.2005.017

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

George Bogoslovsky
Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119992 Moscow, Russia

Received October 06, 2005, in final form November 09, 2005; Published online November 15, 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.

Key words: Lorentz, Poincaré and gauge invariance; spontaneous symmetry breaking; Finslerian space-time.

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