Dirac Strings and the Nonperturbative Photon Propagator in Compact QED

TL;DR

This paper investigates the role of Dirac strings and monopoles in 2+1 dimensional compact QED, showing that Dirac strings are essential for the photon propagator and that photon mass is affected by their presence.

Contribution

It provides a visual representation of monopoles and Dirac strings, and demonstrates through numerical experiments that Dirac strings are crucial for the photon propagator in compact QED.

Findings

Photon mass pole is insensitive to monopole prohibition.

Photon mass nearly vanishes if Dirac strings are prohibited.

Dirac strings generate the photon propagator in compact QED.

Abstract

A ``3D'' Mathematica@-generated picture of monopoles and Dirac strings in $D=2+1$ compact QED is given. In the Villain approximation, the monopole part of the partition function factorizes from the Dirac string part, which generates the photon propagator. Numerical experiments in exact compact QED confirm this result: photon mass pole $M_\gamma$, originally nonzero, is insensitive to monopole prohibition but almost vanishes if Dirac strings are prohibited.