Abstract
We consider the Dirac operator. Its determinant is examined and in two Euclidean dimensions is explicitly evaluated in terms of geometrical quantities. This leads us to consider a generalization of the Wess-Zumino action that is applicable to arbitrary genus. Our analysis is relevant to a number of interesting systems: Schwinger models on curved two-manifolds; string theories with world-sheet vectors; and as an exploration of possible directions in evaluating determinants in four dimensions.
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