  The article contains a review and new results of some mathematical models
relevant to the interpretation of quantum mechanics and emulating well-known
quantum gauge theories, such as scalar electrodynamics (Klein-Gordon-Maxwell
electrodynamics), spinor electrodynamics (Dirac-Maxwell electrodynamics), etc.
In these models, evolution is typically described by modified Maxwell
equations. In the case of scalar electrodynamics, the scalar complex wave
function can be made real by a gauge transformation, the wave function can be
algebraically eliminated from the equations of scalar electrodynamics, and the
resulting modified Maxwell equations describe the independent evolution of the
electromagnetic field. Similar results were obtained for spinor
electrodynamics. Three out of four components of the Dirac spinor can be
algebraically eliminated from the Dirac equation, and the remaining component
can be made real by a gauge transformation. A similar result was obtained for
the Dirac equation in the Yang-Mills field. As quantum gauge theories play a
central role in modern physics, the approach of this article may be
sufficiently general. One-particle wave functions can be modeled as plasma-like
collections of a large number of particles and antiparticles. This seems to
enable the simulation of quantum phase-space distribution functions, such as
the Wigner distribution function, which are not necessarily non-negative.
