On the Implementation of General Background Electromagnetic Fields on a Periodic Hypercubic Lattice

TL;DR

This paper presents a method to implement nonuniform background electromagnetic fields on a periodic hypercubic lattice for lattice QCD calculations, enabling precise studies of electromagnetic properties of hadrons and nuclei.

Contribution

It provides explicit constructions of nonuniform electromagnetic fields on a lattice, including conditions for periodicity and quantization, facilitating advanced electromagnetic property calculations.

Findings

Constructed nonuniform electromagnetic fields on a lattice.

Derived conditions for periodicity and quantization.

Discussed applications to various electromagnetic properties.

Abstract

Nonuniform background electromagnetic fields, once implemented in lattice quantum chromodynamics calculations of hadronic systems, provide a means to constrain a large class of electromagnetic properties of hadrons and nuclei, from their higher electromagnetic moments and charge radii to their electromagnetic form factors. We show how nonuniform fields can be constructed on a periodic hypercubic lattice under certain conditions and determine the precise form of the background U(1) gauge links that must be imposed on the quantum chromodynamics gauge-field configurations to maintain periodicity. Once supplemented by a set of quantization conditions on the background-field parameters, this construction guarantees that no nonuniformity occurs in the hadronic correlation functions across the boundary of the lattice. The special cases of uniform electric and magnetic fields, a nonuniform electric field that varies linearly in one spatial coordinate (relevant to the determination of quadruple moment and charge radii), nonuniform electric and magnetic fields with given temporal and spatial dependences (relevant to the determination of nucleon spin polarizabilities) and plane-wave electromagnetic fields (relevant to the determination of electromagnetic form factors) are discussed explicitly.