Improved automated lattice perturbation theory in background field gauge

TL;DR

This paper introduces an automated algorithm for deriving Feynman rules in lattice perturbation theory within background field gauge, enabling efficient computation of complex vertices and derivatives, especially suited for GPU implementation.

Contribution

It generalizes previous algorithms to handle arbitrary vertices with background and quantum legs, improving automation and computational efficiency in lattice perturbation calculations.

Findings

Automated derivation of Feynman rules for complex lattice actions.

Parallelization techniques significantly speed up calculations.

Enhanced suitability for GPU-based computations.

Abstract

We present an algorithm to automatically derive Feynman rules for lattice perturbation theory in background field gauge. Vertices with an arbitrary number of both background and quantum legs can be derived automatically from both gluonic and fermionic actions. The algorithm is a generalisation of our earlier algorithm based on prior work by L\"uscher and Weisz. We also present techniques allowing for the parallelisation of the evaluation of the often rather complex lattice Feynman rules that should allow for efficient implementation on GPUs, but also give a significant speed-up when calculating the derivatives of Feynman diagrams with respect to external momenta.