Skobeltsyn Institute of Nuclear Physics,

Moscow State University, Moscow, RUSSIA

E-mail: bogoslov@theory.sinp.msu.ru

and

Institute for Theoretical Physics, University of Göttingen,

Göttingen, GERMANY

E-mail: goenner@theorie.physik.uni-goettingen.de

**Generalized Lorentz symmetry and nonlinear spinor fields
in a flat Finslerian space-time**

**Abstract:**

The work is devoted to a 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.