A scheme for determining fundamental interactions and the universality principle

Abstract

The Standard Model of particle physics was established based on the equivalence principle and gauge invariance. The Lagrangians were built upon experimental data demonstrating the violation of discrete symmetries together with ideas of spontaneous symmetry breaking. The features of vector and axial-vector interactions and chirality principle are manually added on in order to fit in the observation data, rather than explained by the model as one may hope. Here we develop a theory of interactions based on the Dirac algebra together with the exterior operations the wedge product and the star operator on the space-time, and develop a scheme for determining all possible interaction formulations. In our scheme, the chirality transformation and the left and right handedness come up naturally. A simple postulate about the universality of physical interactions based on the space-time causal structure yields the attracting features mentioned above as consequences.