A Renormalization Program for Systems with Non-Perturbative Conditions

TL;DR

This paper proposes a new renormalization approach tailored for systems with non-perturbative conditions like boundary effects or background fields, ensuring consistency with these conditions and highlighting subtle differences from standard methods.

Contribution

It introduces a configuration space renormalization program that accounts for non-perturbative conditions, modifying counter-terms accordingly and demonstrating their minimal differences from traditional results.

Findings

Counter-terms differ slightly from standard free space results.

Position-dependent parameters naturally arise due to non-perturbative conditions.

The proposed method remains consistent with physical properties under non-perturbative constraints.

Abstract

In this paper we introduce an alternative renormalization program for systems with non-perturbative conditions. The non-perturbative conditions that we concentrate on in this paper are confined to be either the presence of non-trivial boundary conditions or non-perturbative background fields. We show that these non-perturbative conditions have profound effects on all physical properties of the system and our renormalization program is consistent with these conditions. We formulate the general renormalization program in the configuration space. The differences between the free space renormalization program and ours manifest themselves in the counter-terms as well, which we shall elucidate. The general expressions that we obtain for the counter-terms reduce to the standard results in the free space cases. We show that the differences between these divergent counter-terms are extremely small. Moreover we argue that the position dependences induced on the parameters of the renormalized Lagrangian via the loop corrections, however small, are direct and natural consequences of the non-perturbative position dependent conditions imposed on the system.