$L_\infty$-algebra of braided electrodynamics

TL;DR

This paper develops a braided noncommutative gauge theory for electrodynamics, constructs its algebraic structure, derives equations of motion, and analyzes quantum corrections, revealing unique features like modified charge conservation and UV/IR mixing.

Contribution

It explicitly constructs the braided $L_$-algebra for noncommutative electrodynamics and analyzes its physical and quantum properties.

Findings

Modified charge conservation due to braiding

Presence of UV/IR mixing without non-planar diagrams

Explicit calculation of one-loop vacuum polarization

Abstract

Using the recently developed formalism of braided noncommutative field theory, we construct an explicit example of braided electrodynamics, that is, a noncommutative $U(1)$ gauge theory coupled to a Dirac fermion. We construct the braided $L_\infty$-algebra of this field theory and apply the formalism to obtain the braided equations of motion, action functional and conserved matter current. The braided deformation leads to a modification of the charge conservation. Finally, the Feynman integral appearing in the one-loop contribution to the vacuum polarization diagram is calculated. There are no non-planar diagrams, but the UV/IR mixing appears nevertheless. We comment on this unexpected result.