Lattice Correlation Functions from Differential Equations

TL;DR

This paper explores how differential equations and integration-by-parts techniques from perturbation theory can be used to compute lattice correlation functions, including non-perturbative regimes, demonstrated on scalar $^4$ theory.

Contribution

It introduces a novel application of differential equations and co-homology methods to lattice correlation functions, extending their use beyond perturbative calculations.

Findings

Successful calculation of scalar ^4 correlation functions on small lattices.

Application of differential equations to both Euclidean and Minkowskian signatures.

Extension of perturbation theory techniques to non-perturbative lattice regimes.

Abstract

We discuss how methods developed in the context of perturbation theory can be applied to the computation of lattice correlation functions, in particular in the non perturbative regime. The techniques we consider are integration-by-parts identities (supplemented with symmetry relations) and the method of differential equations, cast in the framework of twisted co-homology. We report on calculations of correlation functions for a scalar $\lambda \phi^4$ theory and lattices of small size, both in Euclidean and Minkowskian signature.