Jacobian subtleties and the complete path-integral bosonization of the non-abelian Thirring model

The non-abelian Thirring model invariant under an arbitrary simple Lie group G is written as a path integral over two bosonic fields taking values in G. The careful computation of the key functional jacobian involved shows that it is a constant, in contrast with the value (a massless fermion determinant in the adjoint representation of G) previously assumed by several authors. We find two exact scale invariant critical points in the model. They are both described by a WZW sigma model of level 2NFlR/φ2. (orig.)