String tension in (2 + 1)-dimensional compact lattice QED: Weak- and strong-coupling results; a variational calculation

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Abstract
The Hamiltonian and wave functions are written as a function of the gauge-invariant magnetic field only. A variational calculation with an ansatz, separable in plaquette space, leads to Mathieu's equation for the wave functions and a self-consistency constraint. This we solve analytically in both the strong- and weak-coupling limit, and we calculate the string tension. We find the electric flux to be confined to a tube of finite radius for all couplings.