New solutions to the Ginsparg-Wilson equation

Abstract

The overlap operator is just the simplest of a class of Dirac operators with an exact chiral symmetry. I demonstrate how a general class of chiral Dirac operators can be constructed, show that they have no fermion doublers and that they are all exponentially local, and test my conclusions numerically for a few examples. However, since these operators are more expensive than the overlap operator, it is unlikely that they will be useful in practical simulations.