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Anomalies of Dirac type operators on Euclidean space

Autor(en)
Alan Carey, Harald Grosse, Jens Kaad
Abstrakt

We develop by example a type of index theory for non-Fredholm operators. A general framework using cyclic homology for this notion of index was introduced in a separate article (Carev and Kaad, Topological invariance of the homological index. arXiv:1402.0475 [math.KT], 2014) where it may be seen to generalise earlier ideas of Carey–Pincus and Gesztesy–Simon on this problem. Motivated by an example in two dimensions in Bollé et al. (J Math Phys 28:1512–1525, 1987) we introduce in this paper a class of examples of Dirac type operators on R

2n that provide non-trivial examples of our homological approach. Our examples may be seen as extending old ideas about the notion of anomaly introduced by physicists to handle topological terms in quantum action principles, with an important difference, namely, we are dealing with purely geometric data that can be seen to arise from the continuous spectrum of our Dirac type operators.

Organisation(en)
Mathematische Physik
Externe Organisation(en)
Australian National University, Université Paris VII - Paris-Diderot
Journal
Communications in Mathematical Physics
Band
335
Seiten
445-475
Anzahl der Seiten
31
ISSN
0010-3616
DOI
https://doi.org/10.1007/s00220-014-2204-9
Publikationsdatum
10-2014
Peer-reviewed
Ja
ÖFOS 2012
103019 Mathematische Physik
ASJC Scopus Sachgebiete
Statistical and Nonlinear Physics, Mathematical Physics
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/0706cba8-01b5-4cec-a7ba-5349663f5417