О НОВЫХ СИММЕТРИЯХ УРАВНЕНИЯ ДИРАКА И ЕГО СИНГУЛЯРНЫХ РЕШЕНИЯХ
ON NEW SYMMETRIES OF DIRAC EQUATION AND ITS SINGULAR SOLUTIONS
We consider some remarkable properties of the Dirac equation for free field related to the connections of its (regular or singular) solutions with those of the Klein-Gordon equation.The latter play the role of potentials for the corresponding Dirac ``field strength'', and the Dirac equation is form invariant under special gauge transformations of the ``potentials''. Moreover, any solution to Dirac equation can be obtained from only a pair of the Klein-Gordon potentials. Under transformations of space-time coordinates the Klein-Gordon potentials can be considered as scalars while associated Dirac fields behave according to a nonlinear representation of Lorentz group, only in a particular case reducing to the canonical bispinor one. Finally, we present some singular solutions to the Dirac and Klein-Gordon equations, one of which possess a finite conserved charge and can be treated as a ``localized de Broglie wave''.