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

TL;DR

This paper introduces a new dynamic disquantization method to derive a classical model of the Dirac particle, revealing internal degrees of freedom and their nonrelativistic nature, without relying on quantum principles.

Contribution

A novel dynamic disquantization procedure is developed to construct a classical analog of the Dirac particle directly from the Dirac equation.

Findings

Classical model S_{Dcl} has ten degrees of freedom.

Internal structure and nonrelativistic internal degrees of freedom are identified.

The method explains why these features were previously undiscovered.

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. Internal degrees of freedom appears to be described nonrelativistically. One discusses interplay between the conventional axiomatic methods and the dynamical methods of the quantum systems investigation. In particular, one discusses the reasons, why the internal degrees of freedom of the Dirac particle and their nonrelativistic character were not discovered during eighty years.