The Origin of Chiral Anomaly and the Noncommutative Geometry

Abstract

We describe the scalar and spinor fields on noncommutative sphere starting from canonical realizations of the enveloping algebra $\mathcal{A}=\mathcal{U}u(2))$. 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 non-perturbatively UV-regular. An exact expresion for the chiral anomaly is found. In the commutative limit the standard formula is recovered.

30 pages

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