Deformation Quantization of Relativistic Particles in Electromagnetic Fields
arXiv:0705.2259 · doi:10.1142/S0217751X08039360
Abstract
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.
43 pages, no figures, harmac file
References in corpus (20)
- Deformation quantization of Poisson manifolds, I
- Features of Time-independent Wigner Functions
- Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space
- Deformation quantization in the teaching of quantum mechanics
- Moyal Quantum Mechanics: The Semiclassical Heisenberg Dynamics
- Noncommutative relativistic particle on the electromagnetic background
- Wigner Trajectory Characteristics in Phase Space and Field Theory
- A New Non-Perturbative Approach to Quantum Theory in Curved Spacetime Using the Wigner Function
- Deformation Quantization of Classical Fields
- The damped harmonic oscillator in deformation quantization
- Deformation Quantization of Bosonic Strings
- Features of Moyal Trajectories
- Quantization of systems with time-dependent constraints. Example of relativistic particle in plane wave
- Quantum deformation of the Dirac bracket
- A Geometrical Approach to Time-Dependent Gauge-Fixing
- Weyl's symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics
- Moyal Quantization for Constrained System
- Semiclassical expansion of quantum characteristics for many-body potential scattering problem
- Weyl-Wigner-Moyal formulation of a Dirac quantized constrained system
- Dirac brackets from magnetic backgrounds