Realization of the Dirac bracket algebras through first class functions and quantization of constrained systems

TL;DR

This paper demonstrates that Dirac bracket algebras can be represented through first class functions and their quantization via star-product, providing a new perspective on constrained systems in classical and quantum mechanics.

Contribution

The work establishes an isomorphism between Dirac bracket algebra and the Poisson algebra of first class functions, and finds its image in the star-product commutator algebra, advancing quantization methods.

Findings

Dirac bracket algebra is isomorphic to the Poisson algebra of first class functions.

The isomorphic image in the star-product commutator algebra is identified.

Provides a framework for quantizing constrained systems using star-products.

Abstract

It is shown that a Dirac bracket algebra is isomorphic to the original Poisson bracket algebra of first class functions subject to first class constraints. The isomorphic image of the Dirac bracket algebra in the star-product commutator algebra is found.