Concerning the generalized Lorentz symmetry and the generalization of the Dirac equation

Abstract

The work is devoted to the generalization of the Dirac equation for a flat locally anisotropic, i.e., Finslerian space-time. At first we reproduce the corresponding metric and a group of the generalized Lorentz transformations, which has the meaning of the relativistic symmetry group of such event space. Next, proceeding from the requirement of the generalized Lorentz invariance we find a generalized Dirac equation in its explicit form. An exact solution of the nonlinear generalized Dirac equation is also presented.

arXiv comment10 pages, 1 figure, to appear in Phys. Lett. A

References in corpus (4)

• Lorentz-Violating Extension of the Standard Model
• CPT Violation and the Standard Model
• Finslerian spaces possessing local relativistic symmetry
• On a Possibility of Phase Transitions in the Geometric Structure of Space-Time

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