A Treatment of the Schwinger Model within Noncommutative Geometry
نویسندگان
چکیده
We describe a free spinor field on a noncommutative sphere starting from a canonical realization of the algebra U(u(2|1)) and a sequence of su(2)-invariant embeddings of su(2) representations. The gauge extension of the model the Schwinger model on a noncommutative sphere is defined and the model is quantized. Due to the noncommutativity of the sphere, the model contains only a finite number of modes, and consequently is non-perturbatively UV-regular. The fermionic determinants and the effective actions are calculated. The origin of chiral anomaly is clarified. In the commutative limit standard formulas are recovered. Supported by the ”Fond zur Förderung der Wissenschaftlichen Forschung in Österreich” project P11783-PHY and by the Slovak Grant Agency VEGA project 1/4305/97.
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