Journal
INTERNATIONAL JOURNAL OF MODERN PHYSICS A
Volume 23, Issue 11, Pages 1757-1790Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217751X08039360
Keywords
deformation quantization; relativistic particles; electromagnetic fields
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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. With in 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 Maxwellfield is quantized in this context.
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