Dirac quantization of noncommutative Abelian Proca field

TL;DR

This paper applies Dirac's Hamiltonian formalism to a noncommutative Abelian Proca field, demonstrating the second class nature of constraints and quantizing the system via Dirac brackets.

Contribution

It extends Dirac's formalism to noncommutative Proca fields and provides a quantization approach for the constrained system.

Findings

Constraints are second class, consistent with non-gauge invariance.

Quantization achieved through Dirac brackets in reduced phase space.

Framework applicable to noncommutative gauge theories.

Abstract

Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not guage invariant. Then, the system of second class constraints is quantized by introducing Dirac brackets in the reduced phase space.