Decoupling of Photon Propagator in Compact QED

TL;DR

This paper demonstrates that in compact QED, the photon propagator mass pole is gauge-variant and not physically meaningful, contrasting with the physical mass scale given by the inverse London penetration depth, as shown through theoretical analysis and numerical simulations.

Contribution

The paper clarifies that the photon propagator mass pole in compact QED is gauge-variant and not physically relevant, challenging assumptions based on Landau-Ginzburg theory.

Findings

Photon propagator mass pole is gauge-variant and physically irrelevant.

Numerical simulations show $M_\gamma$ vanishes when Dirac strings are prohibited.

The inverse London penetration depth remains the physical mass scale.

Abstract

In compact QED$_{2+1}$ quantum monopole fluctuations induce confinement by expelling electric flux in a dual Meissner effect. Guided by Landau-Ginzburg theory, one might guess that the inverse London penetration depth $\lambda^{-1}$---the only physical mass scale---equals the photon propagator mass pole $M_\gamma$. I show this is not true. Indeed, in the Villain approximation the monopole part of the partition function factorizes from the photon part, whose dynamical variables are Dirac strings. Since Dirac strings are gauge-variant structures, I conclude that $M_\gamma$ is physically irrelevant: it is not a blood relative of $\lambda$ or any other quantity in the gauge-invariant sector. This result is confirmed by numerical simulations in the full theory, where $M_\gamma$ is not sensitive to monopole prohibition but essentially vanishes if Dirac strings are prohibited.