An extension of the Weyl-Wigner-Moyal formulation of quantum mechanics suitable for a Dirac quantized constrained system is proposed. In this formulation, quantum observables are described by equivalent classes of Weyl symbols. The Weyl product of these equivalent classes is defined. The new Moyal bracket is shown to be compatible with the Dirac bracket for constrained systems.

Jan 1, 20005 citations

Moyal dynamics of constraint systems

M. I. Krivoruchenko

arXiv:hep-th/0610074Oct 6, 20061 citation

arXiv:quant-ph/0006028 · Physics Letters A

Weyl–Wigner–Moyal formulation of a Dirac quantized constrained system

Domingo J Louis-Martinez

Published May 1, 2000• 5 citations

arXiv HTML PDF

DOI: 10.1016/s0375-9601(00)00275-9

Related papers

Weyl–Wigner–Moyal formalism for Fermi classical systems

I. Galaviz, Hugo García‐Compeán, Maciej Przanowski +1 more

arXiv:hep-th/0612245Annals of PhysicsApr 17, 200714 citations

The Weyl–Wigner–Moyal Formalism on a Discrete Phase Space

Maciej Przanowski, Jaromir Tosiek, Francisco J. Turrubiates

Trends in mathematicsJan 1, 20200 citations

Nonnegative mixed states in Weyl-Wigner-Moyal theory

JoséM. Garcia-Bondia, Joseph C. Várilly

Physics Letters AMar 1, 198824 citations

The Weyl--Wigner--Moyal Formalism. III. The Generalized Moyal Product in the Curved Phase Space

Maciej Przanowski, Jaromir Tosiek

Acta Physica Polonica BFeb 1, 19998 citations

Weyl-Wigner-Moyal formulation of a Dirac quantized constrained system

Louis-Martinez, D

Jan 1, 20005 citations

Moyal dynamics of constraint systems

M. I. Krivoruchenko

Quantization of constraint systems within the Weyl-Wigner-Groenewold-Moyal framework is discussed. Constraint dynamics of classical and quantum systems is reformulated using the skew-gradient projection formalism. The quantum deformation of the Dirac bracket is generalized to match smoothly the classical Dirac bracket in and outside of the constraint submanifold in the limit $\hbar \to 0$ .Quantization of constraint systems within the Weyl-Wigner-Groenewold-Moyal framework is discussed. Constraint dynamics of classical and quantum systems is reformulated using the skew-gradient projection formalism. The quantum deformation of the Dirac bracket is generalized to match smoothly the classical Dirac bracket in and outside of the constraint submanifold in the limit $\hbar \to 0$.

arXiv:hep-th/0610074Oct 6, 20061 citation

\hbar \to 0