The Effect of Reduced Spatial Symmetries on Lattice States: Results for Non-zero Linear Momentum

TL;DR

This paper explores how reducing spatial symmetries affects lattice states with non-zero linear momentum, providing a detailed group-theoretic analysis relevant for interpreting hadron spectra in lattice QCD.

Contribution

It introduces a method to map continuum states to lattice states with non-zero momentum using irreducible representations and Clebsch-Gordan decomposition for the cubic space group.

Findings

Mapped continuum states to lattice states with non-zero momentum

Identified multiparticle states in the hadron spectrum on the lattice

Provided character tables and decomposition techniques for the cubic space group

Abstract

The irreducible representations of the cubic space group are described and used to determine the mapping of continuum states to lattice states with non-zero linear momentum. The Clebsch-Gordan decomposition is calculated from the character table for the cubic space group. These results are used to identify multiparticle states which appear in the hadron spectrum on the lattice.