Massless fermion in 2D space-time

In the path integral approach, the short distance singularity of the two-point function of a quantum field is given by the Green s function corresponding to the classical field equation. By computing the singular term of the Green s function for a massless fermion in two-dimensional curved space-time we show that the short distance limit is not well-defined in general. We determine the necessary condition for the existence of this limit..