Diagrammatic Strong Coupling Expansion of U(1) Lattice Model in Fourier Basis

Abstract

The transfer-matrix of U(1) lattice gauge theory is investigated in the field Fourier space, the basis of which consists of the quantized currents on lattice links. Based on a lattice version of the current conservation, the transfer-matrix elements are shown to be non-zero only between current-states that differ in circulating currents inside plaquettes. In the strong coupling limit, a series expansion is developed for the elements of the transfer-matrix, to which a diagrammatic representation based on the occurrence of virtual link and loop currents can be associated. With $g$ as the coupling, the weight of each virtual current in the expansion is $1/g^2$, by which at any given order the relevant diagrams are determined. Either by interpretation or through their role in fixing the relevant terms, the diagrams are reminiscent of the Feynman ones of the perturbative small coupling expansions.

Comments: v1: 47 pages; 12 Figs; many diagrams as equations! v2: 56 pages. Two sections are added (on spectrum and on lattice-size dependence). Grammar and typos are fixed. Published in PRD 2021