Physics geometrization in microcosm: discrete space-time and relativity theory

Abstract: The presented paper is a review of papers on the microcosm physics geometrization in the last twenty years. These papers develop a new direction of the microcosm physics. It is so-called geometric paradigm, which is alternative to the quantum paradigm, which is conventionally used now. The hypothesis on discreteness of the space-time geometry appears to be more fundamental, than the hypothesis on quantum nature of microcosm. Discrete space-time geometry admits one to describe quantum effects as pure geometric effects. Mathematical technique of the microcosm physics geometrization (geometric paradigm) is based on the physical geometry, which is described completely by the world function. Equations, describing motion of particles in the microcosm, are algebraic (not differential) equations. They are written in a coordinateless form in terms of world function. The geometric paradigm appeared as a result of overcoming of inconsistency of the conventional elementary particle theory. In the suggested skeleton conception the state of an elementary particle is described by its skeleton (several space-time points). The skeleton contains all information on the particle properties (mass, charge, spin, etc.). The skeleton conception is a monistic construction, where elementary particle motion is described in terms of skeleton and world function and only in these terms. The skeleton conception can be constructed only on the basis of the physical geometry. Unfortunately, most mathematicians do not accept the physical geometries, because these geometries are nonaxiomatizable. It is a repetition of the case, when mathematicians did not accept the non-Euclidean geometries of Lobachevsky-Bolyai. As a result this review is a review of papers of one author.