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# Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions

Davoudi, Zohreh, Harrison, James, Jüttner, Andreas, Portelli, Antonin and Savage, Martin J. (2019) Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions. Physical Review D, 99.

Record type: Article

## Abstract

First-principles studies of strongly-interacting hadronic systems using lattice quantum chromodynamics (QCD) have been complemented in recent years with the inclusion of quantum electrodynamics (QED). The aim is to confront experimental results with more precise theoretical determinations, e.g. for the anomalous magnetic moment of the muon and the CP-violating parameters in the decay of mesons. Quantifying the effects arising from enclosing QED in a finite volume remains a primary target of investigations. To this end, finite-volume corrections to hadron masses in the presence of QED have been carefully studied in recent years. This paper extends such studies to the self-energy of moving charged hadrons, both on and away from their mass shell. In particular, we present analytical results for leading finite-volume corrections to the self-energy of spin-0 and spin-$\frac{1}{2}$ particles in the presence of QED on a periodic hypercubic lattice, once the spatial zero mode of the photon is removed, a framework that is called $\mathrm{QED}_{\mathrm{L}}$. By altering modes beyond the zero mode, an improvement scheme is introduced to eliminate the leading finite-volume corrections to masses, with potential applications to other hadronic quantities. Our analytical results are verified by a dedicated numerical study of a lattice scalar field theory coupled to $\mathrm{QED}_{\mathrm{L}}$. Further, this paper offers new perspectives on the subtleties involved in applying low-energy effective field theories in the presence of $\mathrm{QED}_{\mathrm{L}}$, a theory that is rendered non-local with the exclusion of the spatial zero mode of the photon, clarifying recent discussions on this matter.

Text
Theoretical aspects of quantum electrodynamics - Version of Record

Published date: 28 February 2019
Additional Information: 57 pages, 10 figures
Keywords: hep-lat, hep-th

## Identifiers

Local EPrints ID: 429062
URI: https://eprints.soton.ac.uk/id/eprint/429062
ISSN: 1550-7998
PURE UUID: 5148a588-1a72-49ca-a771-f09a702b80ed

## Catalogue record

Date deposited: 20 Mar 2019 17:30

## Contributors

Author: Zohreh Davoudi
Author: James Harrison
Author: Antonin Portelli
Author: Martin J. Savage