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

Abstract

It is shown that the group of generalized Lorentz transformations serves as the 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 an anisotropic fermion-antifermion condensate. The principle of generalized Lorentz invariance enables the exact taking into account of the influence of the 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 equations.