The fermion determinant in two dimensional Minkowski space: Zeros and related properties

We present a detailed analysis of the non-abelian determinant of massless fermions in two dimensional Minkowski space. In the framework of the external field problem, the determinant vanishes if the out- and ingoing vacua are orthogonal; the gauge potentials for which this happens are identified. Causality implies that the effective action obtained from the sum of fermion loops has the right singularity at a zero of the determinant. Such a zero can be reached by a continuous deformation of a potential with non-vanishing determinant. The set of zeros exhibits a rich structure. (orig.)