Singular Perturbations in Quantum Field Theory

TL;DR

This paper introduces a novel approximation method for non-perturbative quantum field theory calculations, leveraging singular perturbation techniques applied to Schwinger equations, with applications to scalar fields, the Gross-Neveu model, and QCD.

Contribution

It proposes a new approximation scheme based on singular perturbation theory for solving Schwinger equations in quantum field models, including QCD.

Findings

Derived non-perturbative solutions for scalar and Gross-Neveu models

Demonstrated the applicability of the method to QCD

Provided insights into the structure of quantum field equations

Abstract

In this talk we discuss a new approximation scheme for non-perturbative calculations in a quantum field theory which is based on the fact that the Schwinger equation of a quantum field model belongs to the class of singularly perturbed equations. The self-interacting scalar field and the Gross-Neveu model are taken as the examples and some non-perturbative solutions of an equation for the propagator are found for these models. The application to QCD is also discussed.