Product rule for gauge invariant Weyl symbols and its application to the semiclassical description of guiding center motion

Abstract

We derive a product rule for gauge invariant Weyl symbols which provides a generalization of the well-known Moyal formula to the case of non-vanishing electromagnetic fields. Applying our result to the guiding center problem we expand the guiding center Hamiltonian into an asymptotic power series with respect to both Planck's constant $\hbar$ and an adiabaticity parameter already present in the classical theory. This expansion is used to determine the influence of quantum mechanical effects on guiding center motion.

24 pages, RevTeX, no figures; shortened version will be published in J.Phys.A