Star-product Description of Quantization in Second-class Constraint Systems

TL;DR

This paper introduces a star-product framework for quantizing second-class constraint systems using the projection operator method, revealing quantum corrections in the operator algebra.

Contribution

It develops a new star-product approach within POM for second-class systems, incorporating nonlocal representations and quantum corrections.

Findings

Defined new star-products for constraint systems

Constructed projected operator-algebra with quantum corrections

Demonstrated noncommutativity effects in operator products

Abstract

The quantization of the second-class constraint systems is discussed within the projection operator method(POM) of constraint systems. Through the nonlocal representation of the constraint hyper-operators, new star-products are defined. Then, the projected operator-algebra of the quantized constraint systems is constructed with these star-products, and it is shown that the commutators and symmetrized products among the projected operators contain the quantum corrections due to the noncommutativity among operators.