Yuri A.Rylov
The distributed system S,
described by the Dirac equation is investigated simply as a dynamic system,
i.e. without usage of quantum principles. The Dirac equation is described in
terms of hydrodynamic variables: 4-flux j, pseudo-vector of the spin s,
an action, and a pseudo-scalar k. In the quasi-uniform approximation,
when all transversal derivatives (orthogonal to the flux vector j) are
small, the dynamic system S turns to a statistical ensemble E of
classical concentrated systems s. Under some conditions the classical
system s describes a classical pointlike particle, moving in a given
electromagnetic field. In general, the world line of the particle is a helix,
even if the electromagnetic field is absent. Both dynamic systems S and E
appear to be non-relativistic in the sense that the dynamic equations written
in terms of hydrodynamic variables are not relativistically covariant with
respect to them, although all dynamic variables are tensors or pseudo-tensors. They
becomes relativistically covariant only after addition of a constant unit
timelike vector f which should be considered as a dynamic variable,
describing a space-time property. This "constant" variable arises
instead of gamma-matrices which are removed by means of zero divizors in the
course of the transformation to hydrodynamic variables. It is possible to
separate out dynamic variables k responsible for quantum effects. It
means that, setting k=0, the dynamic system S described by the
Dirac equation turns to a statistical ensemble E of classical dynamic
systems s.
There is text of the paper in English (pdf ps), in Russian (pdf ps).