A combinatorial derivation of the standard model interactions from the Dirac Lagrangian

Abstract

A composite model of the standard model particles was recently derived using the Dirac Lagrangian on a spacetime where time does not advance along the worldlines of fundamental dust particles, called an ‘internal spacetime’. The aim of internal spacetime geometry is to model certain quantum phenomena using (classical) degenerate spacetime metrics. For example, on an internal spacetime, tangent spaces have variable dimensions, and spin wavefunction collapse is modeled by the projection from one tangent space to another. In this article, we show that the combinatorial structure of the internal Dirac Lagrangian yields precisely the standard model trivalent vertices, together with two new additional (longitudinal) [Formula: see text] vertices that generate the four-valent boson vertices. In particular, we are able to derive electroweak parity violation for both leptons and quarks. We also obtain new restrictions on the possible spin states that can occur in certain interactions. Finally, we determine the trivalent vertices of the new massive spin-[Formula: see text] boson predicted by the model.