Gauge and BRST Generators for Space-Time Non-commutative U(1) Theory

TL;DR

This paper develops Hamiltonian gauge and BRST symmetry generators for space-time non-commutative U(1) gauge theories, utilizing a higher-dimensional formulation and canonical transformations to relate non-commutative and commutative frameworks.

Contribution

It introduces a Hamiltonian formalism for non-local non-commutative gauge theories, including the construction of gauge and BRST generators, and elucidates the Seiberg-Witten map via canonical transformations.

Findings

Constructed Hamiltonian and gauge generators for non-commutative U(1) theory.

Derived the nilpotent BRST charge in the non-commutative setting.

Showed the Seiberg-Witten map as a canonical transformation in superphase space.

Abstract

The Hamiltonian (gauge) symmetry generators of non-local (gauge) theories are presented. The construction is based on the d+1 dimensional space-time formulation of d dimensional non-local theories. The procedure is applied to U(1) space-time non-commutative gauge theory. In the Hamiltonian formalism the Hamiltonian and the gauge generator are constructed. The nilpotent BRST charge is also obtained. The Seiberg-Witten map between non-commutative and commutative theories is described by a canonical transformation in the superphase space and in the field-antifield space. The solutions of classical master equations for non-commutative and commutative theories are related by a canonical transformation in the antibracket sense.