Institute for Problems in Mechanics,
Russian Academy of Sciences,
101-1 Vernadskii Ave.,
Moscow, 119526,
E-mail: rylov@ipmnet.ru

Formalized procedure of transition to classical limit in application to the Dirac equation

Classical model $S_{Dcl}$ of the Dirac particle $S_D$ is constructed. $S_D$ is the dynamic system described by the Dirac equation. For investigation of $S_D$ and construction of $S_{Dcl}$ one uses a new dynamic method: dynamic disquantization. This relativistic purely dynamic procedure does not use principles of quantum mechanics. The obtained classical analog $S_{Dcl}$ is described by a system of ordinary differential equations, containing the quantum constant as a parameter. Dynamic equations for $S_{Dcl}$ are determined by the Dirac equation uniquely. The dynamic system $S_{Dcl}$ has ten degrees of freedom and cannot be a pointlike particle, because it has an internal structure. There are two ways of interpretation of the dynamic system $S_{Dcl}$: (1) dynamical interpretation and (2) geometrical interpretation. In the dynamical interpretation the classical Dirac particle $S_{Dcl}$ is a two-particle structure (special case of a relativistic rotator). It explains freely such properties of $S_{D}$ as spin and magnetic moment, which are strange for pointlike structure. In the geometrical
interpretation the world tube of $S_{Dcl}$ is a ''two-dimensional broken band'', consisting of similar segments. These segments are parallelograms (or triangles), but not the straight line segments as in the case of a structureless particle. Geometrical interpretation of the classical Dirac particle $S_{Dcl}$ generates a new approach to the elementary particle theory.