Noncommuting Electric Fields and Algebraic Consistency in Noncommutative Gauge theories

TL;DR

This paper explores the natural emergence of noncommuting electric fields in $ heta$-expanded noncommutative gauge theories, establishing algebraic consistency via a Hamiltonian generalization of the Seiberg-Witten Map and analyzing gauge symmetries.

Contribution

It introduces a Hamiltonian-based generalization of the Seiberg-Witten Map that ensures algebraic consistency in noncommutative gauge theories and clarifies its role as a canonical transformation.

Findings

Noncommuting electric fields naturally arise in $ heta$-expanded theories.

The generalized Seiberg-Witten Map acts as a canonical transformation.

Gauge symmetries are derived using the Hamiltonian formulation.

Abstract

We show that noncommuting electric fields occur naturally in $\theta$-expanded noncommutative gauge theories. Using this noncommutativity, which is field dependent, and a hamiltonian generalisation of the Seiberg-Witten Map, the algebraic consistency in the lagrangian and hamiltonian formulations of these theories, is established. A comparison of results in different descriptions shows that this generalised map acts as canonical transformation in the physical subspace only. Finally, we apply the hamiltonian formulation to derive the gauge symmetries of the action.