A treatment of the Schwinger Model within Noncommutative Geometry

We describe a free spinor eld on a noncommutative sphere starting from a canonical realization of the algebraU(u(2j1)) 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 dened and the model is quantized. Due to the noncommutativity of the sphere, the model contains only a nite number of modes, and consequently is non-perturbatively UV-regular. The fermionic determinants and the eective actions are calculated. The origin of chiral anomaly is claried. In the commutative limit standard formulas are recovered.