Soliton "dictionary" for massive quantum electrodynamics

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Abstract
The Thirring model and the sine-Gordon theory in two dimensions have been shown to be equivalent. We extend this result by demonstrating the equivalence between massive QED (with self-interacting fermions) and a vector generalization of the sine-Gordon theory. We demonstrate this equivalence by perturbation theory and by constructing the appropriate transformation between the two sets of fields. Because the sine-Gordon equation is known to have classical "kink" or soliton solutions, we are led to suspect that hadrons correspond to extended solutions to the equations of motion in the strong-coupling region.