Multi-particle interpolating operators in quantum field theories with cubic symmetry

TL;DR

This paper introduces a general algorithm for constructing multi-particle interpolating operators in lattice quantum field theories with cubic symmetry, automating the process of combining operators into irreducible representations.

Contribution

The work provides a novel, automated algorithm for creating multi-particle operators respecting cubic symmetry, applicable to various particle types and spins.

Findings

Algorithm successfully automates operator construction.

Applicable to distinguishable and indistinguishable particles.

Implementation is publicly available for use.

Abstract

Numerical studies of lattice quantum field theories are conducted in finite spatial volumes, typically with cubic symmetry in the spatial coordinates. Motivated by these studies, this work presents a general algorithm to construct multi-particle interpolating operators for quantum field theories with cubic symmetry. The algorithm automates the block diagonalization required to combine multiple operators of definite linear momentum into irreducible representations of the appropriate little group. Examples are given for distinguishable and indistinguishable particles including cases with both zero and non-zero spin. An implementation of the algorithm is publicly available at https://github.com/latticeqcdtools/mhi.