Schwinger Equation as Singularly Perturbed Equation

TL;DR

This paper introduces a novel approximation scheme for non-perturbative quantum field theory calculations, focusing on the Schwinger equation's singular nature and connected Green functions, leading to new solutions beyond standard perturbation theory.

Contribution

It proposes a new approximation method for solving the Schwinger equation considering its singularity, and finds non-perturbative solutions in a scalar field model.

Findings

New approximation scheme for Schwinger equation

Non-perturbative solutions in scalar field model

Connection to boundary conditions and Green functions

Abstract

A new approximation scheme for non-perturbative calculations in a quantum field theory is proposed. The scheme is based on investigation of solutions of the Schwinger equation with its singular character taken into account. As a necessary supplementary boundary condition the Green functions' connected structures correspondence principle is used. Besides the usual perturbation theory expansion which is always available as a particular solution of our scheme some non-perturbative solutions of an equation for the propagator are found in the model of a self-interacting scalar field.