On indices of the Dirac operator in a non-Fredholm case

Details On indices of the Dirac operator in a non-Fredholm case On indices of the Dirac operator in a non-Fredholm case

1995-11-16

arxiv.org/abs/hep-th/9511121v2

Mod.Phys.Lett. A11 (1996) 979-986

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, plain latex, no figures. Two definitions supplied and one reference added + some minor corrections, to appear in Mod.

Scientific paper

10.1142/S0217732396001004

The Dirac Hamiltonian with the Aharonov-Bohm potential provides an example of a non-Fredholm operator for which all spectral asymmetry comes entirely from the continuous spectrum. In this case one finds that the use of standard definitions of the resolvent regularized, the heat kernel regularized, and the Witten indices misses the contribution coming from the continuous spectrum and gives vanishing spectral asymmetry and axial anomaly. This behaviour in the case of the continuous spectrum seems to be general and its origin is discussed.

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