Current Renormalization in Finite Volume

Understand

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.