Dirac Operator Normality and Chiral Fermions

Werner Kerler

Chinese Journal of Physics

38卷3S期（2000 / 06 / 01）

623 - 632

英文

Normality of the Dirac operator is shown to be necessary for chiral properties. From the global chiral Ward identity, which in the continuum limit gives the index theorem, a sum rule results which constrains the spectrum. The Ginsparg-Wilson relation is to be restricted to its simple form and is a member of a set of spectral constraints. A family of alternative chiral transformations is introduced. The one of Lüscher is a special case which transports only the anomaly term to the measure. An alternative transformation would also be needed to correct Fujikawa's path-integral approach. From a general function of the hermitean Wilson-Dirac operator the one of Neuberger follows.