On aspects of self-consistency in the Dyson-Schwinger approach to QED and \lambda (\phi^\star \phi)^2 theories

TL;DR

This paper explores the self-consistency of Dyson-Schwinger equations in QED and scalar field theories, establishing their equivalence to many-body perturbation theory and computing non-perturbative solutions.

Contribution

It demonstrates the equivalence of Dyson-Schwinger equations with many-body theory and provides non-perturbative solutions for scalar field gap equations.

Findings

Dyson-Schwinger equations are equivalent to many-body perturbation theory.

Established self-consistent iterative solutions for scalar field gap equations.

Provided non-perturbative solutions in scalar field theories.

Abstract

We investigate some aspects of the self-consistency in the Dyson-Schwinger approach to both the QED and the self-interacting scalar field theories. We prove that the set of the Dyson-Schwinger equations, together with the Green-Ward-Takahashi identity, is equivalent to the analogous set of integral equations studied in condensed matter, namely many-body perturbation theory, where it is solved self-consistently and iteratively. In this framework, we compute the non-perturbative solution of the gap equation for the self-interacting scalar field theory.