Axial anomaly and Ginsparg-Wilson fermions in the Lattice Dirac Sea picture

Details Axial anomaly and Ginsparg-Wilson fermions in the Lattice Dirac Sea picture Axial anomaly and Ginsparg-Wilson fermions in the Lattice Dirac Sea picture

2000-01-14

arxiv.org/abs/hep-lat/0001016v2

Nucl.Phys. B598 (2001) 134-150

Physics

High Energy Physics

High Energy Physics - Lattice

19 pages latex,12 figures; manuscript revised, references added

Scientific paper

10.1016/S0550-3213(00)00772-0

The axial anomaly equation 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 $r$ parameter is necessary to get the correct anomaly. The anomaly is shown to be independent of $r$ for $r>0.5$. The generalization to 3+1 dimensions is also discussed.

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