# Alien Calculus and non perturbative effects in Quantum Field Theory

## TL;DR

This paper discusses using alien calculus and Borel transforms to analyze non-perturbative effects in quantum field theory, exemplified by the two-point function in a massless theory.

## Contribution

It introduces a novel approach employing alien calculus to identify non-perturbative contributions via Borel transform singularities in quantum field theory.

## Key findings

- Alien calculus helps determine non-perturbative effects
- Borel transform singularities reveal non-perturbative contributions
- Application to a massless theory's two-point function

## Abstract

In many domains of physics, methods are needed to deal with non-perturbative aspects. I want here to argue that a good approach is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean \'Ecalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.