On the exact gauge invariant calculation of the fermion determinant in massless two-dimensional QCD

Using heat-kernel methods, we show that factorization of the Dirac operator in two-dimensional QCD allows one to calculate exactly the corresponding functional determinant in an arbitrary gauge for any unitary Lie group. The possibility of achieving this is presented in the form of a theorem on functional determinants which covers a wide class of factorizable operators. In particular we recover inthe light-cone gauge a result recently obtained by Polyakov and Wiegmann. (orig.)