Coordinate space methods for the evaluation of Feynman diagrams in lattice field theory

TL;DR

This paper introduces an efficient coordinate space method for calculating lattice Feynman integrals, especially for massless propagators, demonstrated through explicit two-loop integral computations.

Contribution

It presents a novel recursive approach to evaluate free lattice propagators as linear functions, improving the efficiency of lattice Feynman diagram calculations.

Findings

Recursive evaluation of lattice propagators simplifies calculations

Explicit two-loop integral computations demonstrate method effectiveness

Applicable to massless propagators in infinite volume

Abstract

We describe an efficient position space technique to calculate lattice Feynman integrals in infinite volume. The method applies to diagrams with massless propagators. For illustration a set of two-loop integrals is worked out explicitly. An important ingredient is an observation of Vohwinkel that the free lattice propagator can be evaluated recursively and is expressible as a linear function of its values near the origin.