On the Non-Commutative Geometry of the Electroweak Interaction

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 $C_{\text{C}}^{\mathrm{\infty }}({\mathbb{R}}^4)$ with the Minkowski metric.