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We formulate the U(1) and SU(2) lattice Hamiltonians in a loop-dependent magnetic basis. The formulation is gauge invariant and leads to a differential Schr\"odinger equation whose variables are angles associated with an independent set of closed contours in the lattice. These contours are chosen by solving the Mandelstam identities obeyed by Wilson-loop functionals.
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Bartolo et al. (1989) studied this question.
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