  We describe the classical Schwinger model as a study of the projective
modules over the algebra of complex-valued functions on the sphere. On these
modules, classified by $\pi_2(S^2)$, we construct hermitian connections with
values in the universal differential envelope which leads us to the Schwinger
model on the sphere. The Connes-Lott program is then applied using the Hilbert
space of complexified inhomogeneous forms with its Atiyah-Kaehler structure. It
splits in two minimal left ideals of the Clifford algebra preserved by the
Dirac-Kaehler operator D=i(d-delta). The induced representation of the
universal differential envelope, in order to recover its differential
structure, is divided by the unwanted differential ideal and the obtained
quotient is the usual complexified de Rham exterior algebra over the sphere
with Clifford action on the "spinors" of the Hilbert space. The subsequent
steps of the Connes-Lott program allow to define a matter action, and the field
action is obtained using the Dixmier trace which reduces to the integral of the
curvature squared.
