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

1998/05/31 by Michael Mueller, M Müller
Physics and Astronomy · #Quantum Chromodynamics and Particle Interactions #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #quant-ph

paper · pdf · doi:10.1088/0305-4470/32/6/014

published as J.Phys.A32:1035-1052,1999 · 24 pages, RevTeX, no figures; shortened version will be published in J.Phys.A

arxiv created 1998/11/20 · openalex publication_date 1999/01/01 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/30

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.

Citations

• Quantenmechanik und Gruppentheorie
• The guiding centre approximation in lowest order
• Quantum mechanics as a statistical theory
• On the Quantum Correction For Thermodynamic Equilibrium