On the Non-Commutative Geometry of the Electroweak Interaction

Abstract

In differential geometry, the underlying mathematical structure behind the electroweak theory is a trivial principal $(SU(2)\times U(1))$--bundle over ${\mathbb{R}}^4$ with the Minkowski metric. The aim of this paper is to show that, using non--commutative geometry, the electroweak theory can be described using a trivial quantum principal $SU(2)$--bundle over $C^\infty_\C(\R^4)$ with the Minkowski metric.