Axial anomaly and Ginsparg-Wilson fermions in the lattice Dirac sea picture

The axial anomaly in (1 + 1)-dimensional QED is obtained on the lattice for fermions obeying the Ginsparg-Wilson relation. We make use of the properties of the lattice Dirac sea to investigate the connection between the anomaly and the Ginsparg-Wilson operator in the Hamiltonian picture. The correct anomaly is reproduced for gauge fields whose characteristic time is much larger than the lattice spacing, which is the regime where the adiabatic approximation applies. A non-zero Wilson wr parameter is necessary to get the correct anomaly, The anomaly is shown to be present and independent of r only for r > 0.5. The generalization to 3 + 1 dimensions is also discussed. (C) 2001 Published by Elsevier Science B.V.