2007/05/16 by Laura Sanchez, LAURA SÁNCHEZ, Imelda Galaviz +3
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #hep-th
paper · pdf · doi:10.1142/s0217751x08039360
published as Int.J.Mod.Phys.A23:1757-1790,2008 · 43 pages, no figures, harmac file
arxiv created 2007/05/16 · openalex publication_date 2008/04/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Weyl–Wigner–Moyal formalism for Dirac second-class constrained systems has been proposed recently as the deformation quantization of Dirac bracket. In this paper, after a brief review of this formalism, it is applied to the case of the relativistic free particle. Within this context, the Stratonovich–Weyl quantizer, Weyl correspondence, Moyal ⋆-product and Wigner function in the constrained phase-space are obtained. The recent Hamiltonian treatment for constrained systems, whose constraints depend explicitly on time, are used to perform the deformation quantization of the relativistic free charged particle in an arbitrary electromagnetic background. Finally, the system consisting of a charged particle interacting with a dynamical Maxwell field is quantized in this context.