Decomposition of noncommutative U(1) gauge potential

TL;DR

This paper explores the internal structure of noncommutative U(1) gauge potentials, decomposing them into parts with different transformation properties, and relates them to ordinary gauge fields via Seiberg-Witten mapping.

Contribution

It introduces a novel decomposition of noncommutative gauge potential into gauge and adjoint parts and connects noncommutative and ordinary gauge fields through a new mapping.

Findings

Decomposition reveals inner structure of noncommutative gauge potential.

Gauge potential and field tensor expressed in terms of unit vector field.

Noncommutative gauge fields reduce to ordinary fields at non-singular points.

Abstract

We investigate the decomposition of noncommutative gauge potential $\hat{A_{i}}$, and find it has inner structure, namely, $\hat{A_{i}}$ can be decomposed in two parts $\hat{b_{i}}$ and $\hat{a_{i}}$, here $\hat{b_{i}}$ satisfies gauge transformations while $\hat{a_{i}}$ satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U(1) gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tenser can be expressed in terms of the unit vector field. When the unit vector field has non singularity point, noncommutative gauge potential and gauge field tenser will equal to ordinary gauge potential and gauge field tenser.