Weak coupling expansion of massless QCD with a Ginsparg-Wilson fermion andaxial U(1) anomaly

We discuss the weak coupling expansion of massless QCD with the Dirac opera tor which is derived by Neuberger based on the overlap formalism and satisf ies the Ginsparg-Wilson relation. The axial U(1) anomaly associated to the chiral transformation proposed by Luscher is calculated as an application a nd is shown to have the correct form of the topological charge density for perturbative backgrounds. The coefficient of the anomaly is evaluated as a winding number related to a certain five-dimensional fermion propagator. (C ) 1999 Published by Elsevier Science B.V. All rights reserved.