Current commutator anomalies in finite-element quantum electrodynamics

TL;DR

This paper develops a finite-element lattice formulation of quantum electrodynamics that preserves gauge invariance, avoids species doubling, and naturally regularizes current commutators, aligning lattice results with continuum expectations.

Contribution

It introduces a gauge-invariant, unitary finite-element lattice model for QED that naturally regularizes current commutators without species doubling.

Findings

Lattice current commutators exhibit expected qualitative behavior.

Regularization of current arises naturally from the model.

Lattice results compare favorably with continuum calculations.

Abstract

Four-dimensional quantum electrodynamics has been formulated on a hypercubic Minkowski finite-element lattice. The equations of motion have been derived so as to preserve lattice gauge invariance and have been shown to be unitary. In addition, species doubling is avoided due to the nonlocality of the interactions. The model is used to investigate the lattice current algebra. Regularization of the current is shown to arise in a natural and nonarbitrary way. The commutators of the lattice current are calculated and shown to have the expected qualitative behavior. These lattice results are compared to various continuum calculations. (Five figures available from author.)