Product rule for gauge invariant Weyl symbols and its application to the semiclassical description of guiding centre 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 centre problem we expand the guiding centre Hamiltonian into an asymptotic power series with respect to both Planck's constant and an adiabaticity parameter already present in the classical theory. This expansion is used to determine the influence of quantum-mechanical effects on guiding centre motion.