Calculating the infra-red limit of quantum field theory using analyticity of correlation functions

TL;DR

This paper introduces a novel method leveraging the analyticity of Green functions to compute the infra-red limit of quantum field theories, providing accurate results with minimal perturbative calculations.

Contribution

It presents a new approach to determine infra-red limits in quantum field theories using contour integrals and Borel transforms, applicable to various models.

Findings

Accurately calculates the central charge of minimal models using one-loop perturbation.

Provides estimates for phi^4 theory close to other advanced methods.

Demonstrates the method's effectiveness in different quantum field theory contexts.

Abstract

We describe a general method for calculating the infra-red limit of physical quantities in unitary quantum field theories. Using analyticity of Green functions in a complex scale parameter, the infra-red limit is expressed as a contour integral entirely in the ultra-violet region. The infra-red limit is shown to be the limit of the Borel transform of the physical quantity. The method is illustrated by calculating the central charge of the perturbed unitary minimal models and the critical exponents of phi^4 theory in three dimensions. We obtain approximate values for the central charge which are very close to the exact values using only a one loop perturbative calculation. For phi^4 theory we obtain estimates which are within the errors of other more elaborate approaches.