Conserved Non-Singlet Charges for Staggered Fermion Hamiltonian in 3+1 Dimensions

TL;DR

This paper constructs and analyzes conserved non-singlet charges in a 3+1D staggered fermion Hamiltonian, revealing their algebraic properties and continuum implications.

Contribution

It introduces a novel set of conserved charges derived from lattice symmetries and explores their continuum limit behavior and anomaly implications.

Findings

Charges exhibit non-commutativity on the lattice

Charges generate axial SU(2)_L × SU(2)_R transformations in the continuum

Implications for anomalies are discussed

Abstract

We study conserved charges of the staggered fermion Hamiltonian in 3+1 dimensions. By decomposing staggered fermions into Majorana components and exploiting lattice translation symmetries, we construct a set of conserved non-singlet charges. We analyze their algebra andshow that, although the charges exhibit nontrivial non-commutativity on the lattice, they generate axial SU(2)_L \tines SU(2)_R transformations for low-energy degrees of freedom in the continuum limit. Possible implications for anomalies are discussed.