Talk presented by Werner Kerler
Parallel Session: Chiral Fermions I
Tuesday June 29th, 15.50 - 16.10, Room 7
Dirac operator normality and chiral properties
Abstract: Normality in connection with $\gamma_5$-hermiticity gives the basic chiral properties and rules. The Ginsparg-Wilson (GW) relation is just one out of the allowed constraints on the spectrum. The sum rule for chiral differences of real modes also occurs in the Ward identity related to the global chiral transformation. It follows in a general way that the alternative transformation of L\"uscher gives the same Ward identity as the usual chiral one, in the global and in the local case. The derivation, in which normality is imposed on a general function of the hermitean Wilson-Dirac (HWD) operator, inevitably leads at same time to the Neuberger operator and to the GW relation. In this context also the case with zero eigenvalues of the HWD operator is handled. The eigenvalue flows of the HWD operator obey a differential equation, the solutions of which show characteristic features.
Massimo Campostrini,
campo@mailbox.difi.unipi.it