A Wigner quasi-distribution function for charged particles in classical electromagnetic fields

A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relat ion to the axial gauge is discussed, as well as the relation between the ki netic and canonical momenta in the Wigner representation. Gauge-invariant q uantum analogs of Hamilton-Jacobi and Boltzmann kinetic equations are formu lated for arbitrary classical electromagnetic fields in terms of the "slash ed" derivatives and momenta, introduced for this purpose. The kinetic meani ng of these slashed quantities is discussed. We introduce gauge-invariant c onditional moments and use them to derive a kinetic momentum continuity equ ation. This equation provides us with a hydrodynamic representation for qua ntum transport processes and a definition of the "collision force." The hyd rodynamic equation is applied for the rotation part of the electron motion, The theory is illustrated by its application in three examples: Wigner qua si-distribution function and equations for an electron in a magnetic field and harmonic potentials Wigner quasi-distribution function for a charged pa rticle in periodic systems using the kq representation two Wigner quasi-dis tribution functions for heavy-mass polaron in an electric field. (C) 2001 A cademic Press.