Braided Quantum Electrodynamics

TL;DR

This paper develops a braided noncommutative version of quantum electrodynamics using homotopy algebra, deriving equations, conserved currents, and correlation functions, and finds it lacks UV/IR mixing and non-planar diagrams.

Contribution

It introduces a braided $L_$-algebra framework for electrodynamics, providing explicit equations, conserved currents, and a new approach to correlation functions without UV/IR mixing.

Findings

Braided electrodynamics formulated with explicit equations and conserved currents.

Correlation functions computed without UV/IR mixing.

Absence of non-planar diagrams in the braided theory.

Abstract

The homotopy algebraic formalism of braided noncommutative field theory is used to define the explicit example of braided electrodynamics, that is, $\mathsf{U}(1)$ gauge theory minimally coupled to a Dirac fermion. We construct the braided $L_\infty$-algebra of this field theory and obtain the braided equations of motion, action functional and conserved matter current. The modifications of the electric charge conservation law due to the braided noncommutative deformation are described. We develop a braided generalization of Wick's theorem, and use it to compute correlation functions of the braided quantum field theory using homological perturbation theory. Our putative calculations indicate that the braided theory does not contain the non-planar Feynman diagrams of conventional noncommutative quantum field theory, and that correlators do not exhibit UV/IR mixing.