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

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

2005-11-25

arxiv.org/abs/math-ph/0511077v1

SIGMA 1 (2005), 017, 9 pages

Physics

Mathematical Physics

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2005.017

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.

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