Renormalization in spherical field theory

TL;DR

This paper develops a non-perturbative renormalization approach within the spherical field formalism, successfully removing divergences and maintaining invariance, exemplified by massless phi^4 theory in four dimensions.

Contribution

It introduces a method for non-perturbative renormalization using local counterterms in the spherical field formalism, ensuring finiteness and translational invariance.

Findings

All ultraviolet divergences are removed with local counterterms.

The renormalized theory remains finite and translationally invariant.

Application to massless phi^4 theory demonstrates the method's effectiveness.

Abstract

We derive several results concerning non-perturbative renormalization in the spherical field formalism. Using a small set of local counterterms, we are able to remove all ultraviolet divergences in a manner such that the renormalized theory is finite and translationally invariant. As an explicit example we consider massless phi^4 theory in four dimensions.