2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/186003We 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.AQuantum Physicstext