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 spacetime. 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.
 Publication:

Physics Letters A
 Pub Date:
 March 2004
 DOI:
 10.1016/j.physleta.2004.01.040
 arXiv:
 arXiv:hepth/0402172
 Bibcode:
 2004PhLA..323...40B
 Keywords:

 Finslerian spacetime;
 Dirac equations;
 Lorentz;
 PoincarĂ© and gauge invariance;
 Spontaneous symmetry breaking;
 High Energy Physics  Theory
 EPrint:
 10 pages, 1 figure, to appear in Phys. Lett. A