Scale Setting for Self-consistent Backgrounds

TL;DR

This paper proposes a novel scale-setting method for self-consistent backgrounds in quantum field theory, addressing ambiguities and conservation issues by introducing a scale-field at the effective action level.

Contribution

It introduces a new scale-field framework for setting the renormalization scale, ensuring consistency and conservation in quantum field theory backgrounds.

Findings

The scale-field approach avoids stress-energy non-conservation.

Application demonstrated in scalar and gravitational theories.

Addresses conceptual ambiguities in scale setting.

Abstract

The quest for finding self-consistent background solutions in quantum field theory is closely related to the way one decides to set the renormalization scale $k$. This freedom in the choice of the scale setting can lead to ambiguities and conceptual inconsistencies such as the non-conservation of the stress-energy tensor. In this paper a setting for the "scale-field" is proposed at the level of effective action, which avoids such inconsistencies by construction. The mechanism and its potential is exemplified for scalar $\phi^4$ theory and for Einstein-Hilbert-Maxwell theory.