Institute of Physics, NAS of Ukraine

46 Nauky Ave. 46, Kyiv 03028, UKRAINE

E-mail: sem@iop.kiev.ua

*Bohdan LEV, Constantin
USENKO*

Chair of Theoretical Physics, Department of Physics,

Kyiv National Shevchenko University,

2,b1, acad. Glushkova prospect, Kyiv, UKRAINE

E-mail: lev@iop.kiev.ua, blev@i.kiev.ua, usenko@phys.univ.kiev.ua,
usenko@ups.kiev.ua

**Quantum phase space in relativistic theory: the case
of charge-invariant observables**

**Abstract:**

Mathematical method of quantum phase space is very useful in physical
applications like quantum optics and non-relativistic quantum mechanics.
However, attempts to generalize it for the relativistic case lead to some
difficulties. One of problems is band structure of energy spectrum for
a relativistic particle. This corresponds to an internal degree of freedom,
so-called charge variable. In physical problems we often deal with such
a kind of dynamical variables that do not depend on this degree of freedom.
These are position, momentum, and any combination of them. Restricting
our consideration to this kind of observables we propose the relativistic
Weyl-Wigner-Moyal formalism, which contains some surprising differences
from its non-relativistic counterpart.