Institute for Problems in Mechanics,

Russian Academy of Sciences,

101-1 Vernadskii Ave.,

Moscow, 119526,

RUSSIA

E-mail: rylov@ipmnet.ru

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

**Abstract:**

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.