Self-consistent field approximation for string tension in SU(2) lattice gauge theory

We devise a self-consistent field approximation for Hamiltonian pure SU(2) lattice gauge theory in 2+1 dimensions. The approximation is suitable for estimating the string tension between two static color spin-1/2 charges. After treating gauge arbitrariness and characterizing the two charge states, we adopt a trial state having two arbitrary wave functions for each plaquettelike degree of freedom. Variational equations for these wave functions have a self-consistent field character in that each plaquette moves in a potential determined by all others. The mechanism of color flux-tube formation is identified, and the problem is reduced to a simple lattice calculation