Greens function of a free massive scalar field on the lattice

TL;DR

This paper introduces a high-precision numerical method to compute the Greens function of a free massive scalar field on a lattice, utilizing recursive relations with the massless Greens function for masses less than 2.

Contribution

The authors develop a recursive approach to efficiently calculate the Greens function for massive scalar fields on the lattice, improving precision and computational simplicity.

Findings

Accurate recursive formulas for Greens functions with m<2

High-precision numerical results achieved

Simplified computation using massless Greens function

Abstract

We propose a method to calculate the Greens function of a free massive scalar field on the lattice numerically to very high precision. For masses m < 2 (in lattice units) the massive Greens function can be expressed recursively in terms of the massless Greens function and just two additional mass-independent constants.