Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-11-08
Rev.Math.Phys.9:689-718,1997
Physics
High Energy Physics
High Energy Physics - Theory
34 pages, Latex, submitted for publication
Scientific paper
10.1142/S0129055X97000257
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.
da Silva Amaro Rica
Mignaco Juan A.
Sigaud C.
Vanhecke F. J.
No associations
LandOfFree
The Connes-Lott program on the sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Connes-Lott program on the sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Connes-Lott program on the sphere will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-291033