1995/02/14 by P. Zhuang, U. Heinz, Ulrich Heinz · 110 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Constraint (computer-aided design) #Covariant transformation #Gas Dynamics and Kinetic Theory #Kinetic energy #Mathematical physics #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum electrodynamics #Quantum mechanics #Scalar (mathematics) #Spinor #nucl-th
paper · pdf · doi:10.1006/aphy.1996.0011
published in Annals of Physics 245(2), 311-338 (Elsevier BV) · 32 pages, no figures, standard Latex
arxiv created 1995/02/14 · openalex publication_date 1996/02/01 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the relationship between the covariant and the three-dimensional (equal-time) formulations of quantum kinetic theory. We show that the three-dimensional approach can be obtained as the energy average of the covariant formulation. We illustrate this statement in scalar and spinor QED. For scalar QED we derive Lorentz covariant transport and constraint equations directly from the Klein-Gordon equation rather than through the previously used Feshbach-Villars representation. We then consider pair production in a spatially homogeneous but time-dependent electric field and show that the pair density is derived much more easily via the energy averaging method than in the equal-time representation. Proceeding to spinor QED, we derive the covariant version of the equal-time equation derived by Bialynicki-Birula et al. We show that it must be supplemented by another self-adjoint equation to obtain a complete description of the covariant spinor Wigner operator. After spinor decomposition and energy average we study the classical limit of the resulting three-dimensional kinetic equations. There are only two independent spinor components in this limit, the mass density and the spin density, and we derive also their covariant equations of motion. We then show that the equal-time kinetic equation provides a complete description only for constant external electromagnetic fields, but is in general incomplete. It must be supplemented by additional constraints which we derive explicitly from the covariant formulation.