Long-distance behaviour of fermion propagators in the chiral Schwinger model

The chiral Schwinger model's fermionic sector is studied by comparing the fermion propagator of the original Jackiw-Rajaraman formulation with a propagator in the gauge invariant formulation. The main difference consists in the existence of fermionic single particle states in the original formulation, while there are no such states in the gauge invariant formulation. It is suggested that this difference is caused by renormalization, which changes the Hilbert space.