The origin of chiral anomaly and the noncommutative geometry

We describe scalar and spinor fields on a noncommutative sphere starting from canonical realizations of the enveloping algebra A = U (u(2)). The gauge extension of a free spinor model, the Schwinger model on a noncommutative sphere, is defined and the model is quantized. The noncommutative version o...

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Bibliographic Details
Published in:Journal of mathematical physics 2000-05, Vol.41 (5), p.2789-2804
Main Author: Prešnajder, P.
Format: Article
Language:English
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Summary:We describe scalar and spinor fields on a noncommutative sphere starting from canonical realizations of the enveloping algebra A = U (u(2)). The gauge extension of a free spinor model, the Schwinger model on a noncommutative sphere, is defined and the model is quantized. The noncommutative version of the model contains only a finite number of dynamical modes and is nonperturbatively UV regular. An exact expression for the chiral anomaly is found. In the commutative limit the standard formula is recovered.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.533271