Space-geometric Interpretation of Standard Model Fermions

Based on the geometric interpretation of the Dirac equation as an evolution equation on the three-dimensional exterior bundle Λ(R), we propose the bundle (T ⊗Λ⊗Λ)(R) as a geometric interpretation of all standard model fermions. The generalization to curved background requires an ADM decomposition M ∼= M × R and gives the bundle (T ⊗ Λ ⊗ Λ)(M). 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 ∗ operator. The space-geometric interpretation leads to different physical predictions about the connection of SM with gravity, but gives no such differences on Minkowski background.