Space-geometric interpretation of standard model fermions

Abstract

Based on the geometric interpretation of the Dirac equation as an evolution equation on the three-dimensional exterior bundle /(R^3), we propose the bundle (T x / x /)(R^3) as a geometric interpretation of all standard model fermions. The generalization to curved background requires an ADM decomposition M^4=M^3 x R and gives the bundle (T x / x /)(M^3). As a consequence of the geometric character of the bundle there is no necessity to introduce a tetrad or triad formalism. Our space-geometric interpretation associates colors as well as fermion generations with directions in space, electromagnetic charge with the degree of a differential form, and weak interactions with the Hodge star operator. The space-geometric interpretation leads to different physical predictions about the connection of the SM with gravity, but gives no such differences on Minkowski background.