Eur. Phys. J. C 20, 185-191
DOI: 10.1007/s100520100623

Reconstruction of the standard model in a generalized differential geometry based on the real structure

Y. Okumura¹, H. Kase² and K. Morita<sup>3

1</sup>  Department of Physics, Boston University, Boston, MA 02215, USA
²  Department of Physics, Daido Institute of Technology, Nagoya, 457, Japan
³  Department of Physics, Nagoya University, Nagoya, 464-01, Japan

(Received: 31 January 2000 / Revised version: 28 July 2000 / Published online: 25 April 2001 -© Springer-Verlag / Società Italiana di Fisica 2001)

Abstract
The standard model is reconstructed in a generalized differential geometry (GDG) based on the idea of a real structure as proposed by Coquereaux et al. and Connes. The GDG considered in this article is a kind of non-commutative geometry (NCG) on the discrete space that successfully reproduces the Higgs mechanism of the spontaneously broken gauge theory. Here, a GDG is a direct generalization of the differential geometry on an ordinary continuous manifold to the product space of this manifold with a discrete manifold. In a GDG, a one-form basis on the discrete space is incorporated in addition to the one-form basis on Minkowski space, rather than as in Connes's original work. Although the Lagrangians obtained in this way are the same as those obtained in our previous formulation of GDG, the basic formalism becomes very simply and clear.

© Società Italiana di Fisica, Springer-Verlag 2001