Current Renormalization in Finite Volume

TL;DR

This paper investigates how conserved currents in finite volume field theories are additively renormalized due to infrared effects, demonstrating the phenomenon specifically for pions within chiral perturbation theory coupled to electromagnetism.

Contribution

It introduces gauge invariant effective theories that explain current renormalization from zero mode operators, aligning with Ward identities and low-energy theorems.

Findings

Conserved currents are additively renormalized in finite volume due to infrared effects.

Zero mode operators in effective theories account for current renormalization.

No conflicts with Ward identities or low-energy theorems are observed.

Abstract

For finite volume field theories with discrete translational invariance, conserved currents can be additively renormalized by infrared effects. We demonstrate this for pions using chiral perturbation theory coupled to electromagnetism in a periodic box. Gauge invariant single particle effective theories are constructed to explain these results. In such theories, current renormalization arises from operators involving the zero mode of the gauge field. No contradictions with Ward identities, or low-energy theorems are encountered.