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Anomalies and Schwinger terms in NCG field theory models
KTH, Superseded Departments, Physics.
2001 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 42, no 10, 4779-4801 p.Article in journal (Refereed) Published
Abstract [en]

We study the quantization of chiral fermions coupled to generalized Dirac operators arising in NCG Yang-Mills theory. The cocycles describing chiral symmetry breaking are calculated. In particular, we introduce a generalized locality principle for the cocycles. Local cocycles are by definition expressions which can be written as generalized traces of operator commutators. In the case of pseudodifferential operators, these traces lead in fact to integrals of ordinary local de Rham forms. As an application of the general ideas we discuss the case of noncommutative tori. We also develop a gerbe theoretic approach to the chiral anomaly in the Hamiltonian quantization of NCG field theory.

Place, publisher, year, edition, pages
2001. Vol. 42, no 10, 4779-4801 p.
Keyword [en]
quantization, operators, fermions, bundle
URN: urn:nbn:se:kth:diva-20945ISI: 000171066700009OAI: diva2:339642
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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