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

Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences
 101-1 ,Vernadskii Ave., Moscow, 119526, Russia
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Updated July 25, 2005


Classical model S_Dcl of the Dirac particle S_ is constructed. S_ is the dynamic system described by the Dirac
equation. For investigation of S_ 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.

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