THE LORENTZ GROUP IS A BASE FOR DESCRIBING INTERACTION OF BOSONS AND FERMIONS WITH PSEUDO-RIEMANNIAN STRUCTURE OF A BACKGROUND SPACE-TIME. WHAT SHOULD BE INSTEAD FOR FINSLERIAN SPACE-TIME MODELS?
2012jsq | Red'kov V.M., Kisel V.V., Ovsiyuk E.M.  // Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus; Belarus State Pedagogical University, Minsk, Belarus; Mozyr State Pedagogical University, Mozyr, Belarus, v.redkov@dragon.bas-net.by, e.ovsiyuk@mail.ru

A brief overview of the basics of the theory of wave equations of elementary particles in the presence of external gravitational field, described as a pseudo-Riemannian structure of space-time, is given. Covariant generalization of the wave equations, set in Minkowski space, are presented for bosons and fermions equally, is presented as the result of a single tetrad recipe by Tetrode-Weyl-Fock-Ivanenko, based on representations of the Lorentz group. The Lorentz group plays a unifying role in describing the fields of all particles (with different spins, massive and massless) in the flat and in curved space-time. The difference lies in the fact that in flat space Lorentz group acts as a global symmetry of the wave equations; and in a pseudo-Riemannian space, it plays a role of local symmetry group (dependent on coordinates). Particular attention is given to the Dirac and Maxwell fields. Because any new theory of physical space-time can be expected to cover already developed and proven models, the question naturally arises: for what should be replaced the method of describing the interactions of elementary particles with a pseudo-Rimannian geometric background, if the space-time endowed with a Finsler structure.The answer to this question, if possible, should be fairly universal and independent of the magnitude of the spin of a particle or its mass. The general answer to this question would provide us with the better understanding what we can expect in physics from the use of Finsler geometry, in the most radical aspect as a basic new geometry of physical space-time.One can also put a more particular question: what effective physical media can be described by using a generalized Maxwell electrodynamics in space-time with Finsler geometry.

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