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''.

Authors

Conference proceedings

Publisher

РУДН

Language

Russian

Pages

46-50

Status

Published

Year

2018

Organizations

^{1}Peoples' Friendship University of Russia

Date of creation

07.11.2019

Date of change

07.11.2019

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LIV All-Russia conference on problems in dynamics, particle physics, plasma physics and optoelectronics. Moscow, Russia, 14-17 may 2018 г..
РУДН.
2018.
P. 39-42

Article

LIV All-Russia conference on problems in dynamics, particle physics, plasma physics and optoelectronics. Moscow, Russia, 14-17 may 2018 г..
РУДН.
2018.
P. 92-93