Abstract:
Qualitative features of Ginsparg-Wilson fermions, as
formulated by Neuberger, coupled to two dimensional U(1)
gauge theory are studied. The role of the Wilson mass
parameter in changing the number of massless flavors in the
theory and its connection with the index of the Dirac
operator is studied. Although the index of the Dirac
operator is not related to the geometric definition of the
topological charge for strong couplings, the two start to
agree as soon as one goes to moderately weak couplings. This
produces the desired singularity in the quenched chiral
condensate which appears to be very difficult to reproduce
with staggered fermions. The fermion determinant removes the
singularity and reproduces the known chiral condensate and
the meson mass within understandable errors.
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