Lattice Regularization and Symmetries

TL;DR

This paper presents a general method to derive lattice symmetry transformations from continuum symmetries, addressing the complex relationship exemplified by chiral symmetry and ensuring lattice actions retain continuum symmetries.

Contribution

It introduces a systematic procedure to determine lattice symmetry transformations from continuum symmetries, facilitating symmetry preservation in lattice formulations.

Findings

Provides a general framework for lattice symmetry transformations

Ensures lattice actions inherit continuum symmetries

Addresses challenges exemplified by chiral symmetry

Abstract

Finding the relation between the symmetry transformations in the continuum and on the lattice might be a nontrivial task as illustrated by the history of chiral symmetry. Lattice actions induced by a renormalization group procedure inherit all symmetries of the continuum theory. We give a general procedure which gives the corresponding symmetry transformations on the lattice.