Analytic results for Schwinger--Dyson equations with a mass term

TL;DR

This paper derives and solves Schwinger--Dyson equations for massive Yukawa and Wess--Zumino-like models, providing explicit IR solutions and parametric UV solutions, advancing understanding of non-supersymmetric and supersymmetric quantum field theories.

Contribution

It introduces a method to derive and solve linear Schwinger--Dyson equations with mass terms in both non-supersymmetric and supersymmetric models, including explicit IR and UV solutions.

Findings

Explicit IR solutions for non-supersymmetric models

Parametric UV solutions for both models

Extension of Schwinger--Dyson analysis to massive theories

Abstract

Using kinematic renormalization, we derive the Schwinger--Dyson equations for a massive Yukawa model and a Wess--Zumino-like one. Both have linear Schwinger--Dyson equations and a massive renormalized particle. An explicit solution is found in the IR limit of the non-supersymmetric case. Parametric solutions are found in the UV limit of the same model and for the supersymmertic model.