This analysis shows how gauge transformations influence potentials in compact QED under different boundary conditions.
We show that the hamiltonian formalism of compact QED on the lattice gauge transformations appear as representations of translations on a circle or on a line according to the boundary conditions on the wave functions. When gauge invariance is enforced, one gets at strong coupling a linear potential in the first case and a Coulombic potential in the second.
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De et al. (1993) studied this question.
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