Modified $U(1)$ lattice gauge theory: towards realistic lattice QED

TL;DR

This study investigates a modified 4D U(1) lattice gauge theory without monopoles, demonstrating the absence of phase transitions, massless photons, and stable state ratios, with improved state overlaps through further modifications.

Contribution

It introduces a monopole-free U(1) lattice gauge theory and analyzes its properties, showing no phase transition and improved state overlaps, advancing the understanding of lattice QED models.

Findings

No phase transition for 0 < β ≤ 2

Photon remains massless and matches free field theory

Stable ratios of scalar, vector, tensor state energies

Abstract

We study properties of the compact $~4D~$ $U(1)$ lattice gauge theory with monopoles {\it removed}. Employing Monte Carlo simulations we calculate correlators of scalar, vector and tensor operators at zero and nonzero momenta $~\vec{p}~$. We confirm that the theory without monopoles has no phase transition, at least, in the interval $~0 < \beta \leq 2~$. There the photon becomes massless and fits the lattice free field theory dispersion relation very well. The energies of the $~0^{++}~$, $~1^{+-}~$ and $~2^{++}~$ states show a rather weak dependence on the coupling in the interval of $~\beta~$ investigated, and their ratios are practically constant. We show also a further modification of the theory suppressing the negative plaquettes to improve drastically the overlap with the lowest states (at least, for $~J=1$).