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

V. G. Bornyakov·V. K. Mitrjushkin·M. Müller-Preussker
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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 $~0 < β\leq 2~$. 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 $~β~$ 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 $~J=1$).

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V. G. Bornyakov, V. K. Mitrjushkin, M. Müller-Preussker. 1992-09-23. Modified $U(1)$ lattice gauge theory: towards realistic lattice QED. https://arxiv.org/abs/hep-lat/9209023

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