Quantum deformation of the Dirac bracket
M.I. Krivoruchenko (Moscow, ITEP & Tubingen U.), A.A. Raduta (Tubingen, U. & Bucharest U. & Bucharest, IFIN-HH), Amand Faessler (Tubingen U.)
TL;DR
This paper develops a quantum deformation of the Dirac bracket, extending the Moyal bracket to systems with second-class constraints and gauge invariance, enabling better quantization of constrained systems.
Contribution
It introduces a quantum deformation of the Dirac bracket applicable to systems with second-class constraints and gauge invariance, generalizing the Moyal bracket.
Findings
Constructed a quantum Dirac bracket for constrained systems.
Extended the Moyal bracket to second-class and gauge-invariant systems.
Provides a framework for quantizing constrained classical systems.
Abstract
The quantum deformation of the Poisson bracket is the Moyal bracket. We construct quantum deformation of the Dirac bracket for systems which admit global symplectic basis for constraint functions. Equivalently, it can be considered as an extension of the Moyal bracket to second-class constraints systems and to gauge-invariant systems which become second class when gauge-fixing conditions are imposed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.