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Anomalies and Schwinger Terms in NCG Field Theory Models
Author(s) -
Mickelsson J.
Publication year - 2002
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/1521-3978(200205)50:5/7<705::aid-prop705>3.0.co;2-n
Subject(s) - noncommutative geometry , principle of locality , locality , quantization (signal processing) , mathematics , torus , class (philosophy) , pure mathematics , operator (biology) , mathematical physics , field (mathematics) , symmetry (geometry) , quantum field theory , dirac (video compression format) , theoretical physics , algebra over a field , physics , quantum , quantum mechanics , computer science , philosophy , algorithm , repressor , artificial intelligence , linguistics , chemistry , biochemistry , geometry , transcription factor , quantum nonlocality , quantum entanglement , neutrino , gene
This talk is based on the paper [1], which contains references to the original literature. 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 take the case of noncommutative tori.