On indices of the Dirac operator in a non-Fredholm case
نویسنده
چکیده
The Dirac Hamiltonian with the Aharonov-Bohm potential provides an example of a nonFredholm 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. PACS numbers : 11.30.Pb, 02-30.Tb, 03-65.Bz e-mail address : [email protected], [email protected] On leave from Institute of Physics, Na Slovance 2, CZ-180 40 Praha 8, Czech Republic
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