Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model

We present a numerical study of the properties of the Fixed Point lattice Dirac operator in the Schwinger model. We verify the theoretical bounds on the spectrum, the existence of exact zero modes with definite chirality, and the Index Theorem. We show by explicit computation that it is possible to find an accurate approximation to the Fixed Point Dirac operator containing only very local couplings