The Hamiltonian BRST quantization of a noncommutative nonabelian gauge theory and its Seiberg-Witten map

TL;DR

This paper develops a Hamiltonian BRST quantization framework for noncommutative nonabelian gauge theories, establishing a Seiberg-Witten map for phase-space variables and demonstrating the consistency of gauge structures between original and mapped theories.

Contribution

It provides a first-order Seiberg-Witten map for all phase-space variables in noncommutative gauge theories and shows their gauge structure equivalence.

Findings

Existence of a complete Seiberg-Witten map for phase-space variables.

Canonical derivation of gauge structure correspondence.

Consistency between original and mapped gauge theories.

Abstract

We consider the Hamiltonian BRST quantization of a noncommutative non abelian gauge theory. The Seiberg-Witten map of all phase-space variables, including multipliers, ghosts and their momenta, is given in first order in the noncommutative parameter $\theta$. We show that there exists a complete consistence between the gauge structures of the original and of the mapped theories, derived in a canonical way, once we appropriately choose the map solutions.