Perturbation calculation of the axial anomaly of Ginsparg-Wilson fermion

Abstract

We evaluate the axial anomaly for the general Ginsparg-Wilson fermion operator $D=D_c(\text{Id}+R{D}_c{)}^{-1}$ with $R=r\text{Id}$. For any chirally symmetric $D_c$ which in the free fermion limit, is free of species doubling and behaves like $i{\gamma }_{\mu }{p}_{\mu }$ as $p\to 0$, the axial anomaly $\text{tr}[{\gamma }_5(RD)(x,x)]$ for U(1) lattice gauge theory with single fermion flavor is equal to $e^2/(32{\pi }^2){ϵ}_{\mu \nu \lambda \sigma }{F}_{\mu \nu }(x)F_{\lambda \sigma }(x+\hat{\mu }+\hat{\nu })$ plus terms which are higher orders and/or non-perturbative contribtuons. The $F\tilde{F}$ term is r-invariant and has the correct continuum limit.

Comments: 38 pages, latex, 1 figure, add appendix C and several remarks