Systematic Analytic Regularization in $\varphi^4$ and Yukawa Theories

TL;DR

The paper presents a new regularization method called Systematic Analytic Regularization (SAR) that ensures finiteness of quantum field theories at the action level by analytic continuation.

Contribution

SAR is a novel regularization scheme that regularizes theories at the action level by analytic continuation of the kinetic operator's power, demonstrated in $$ and Yukawa theories.

Findings

SAR fully regularizes $$ and Yukawa theories at NLO.

SAR ensures theories are finite before Dyson series evaluation.

The method is self-consistent and systematic.

Abstract

We introduce a novel regularization scheme: Systematic Analytic Regularization (SAR). SAR regularizes a theory at the level of the action by analytically continuing the power of the kinetic operator, ensuring that the theory is formally finite before any terms in the Dyson series are evaluated. We demonstrate that SAR fully and self-consistently regularizes $\varphi^4$ and Yukawa theories at NLO.