Path-integral solubility of two-dimensional models

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Abstract
We apply the technique of Fujikawa to solve for simple two-dimensional models by looking at the nontrivial transformation properties of the fermion measure in the path-integral formalism. We obtain the most general solution for the massless Thirring model and point out how the one-parameter solution reduces to that of Johnson and Sommerfield in a particular limit. We present the most general solution for the massive vector model indicating how it reduces to the solutions of Brown and Sommerfield for different values of the parameter. The solution of a gradient-coupling model is also discussed.