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

TL;DR

This paper derives the standard model interactions from a novel internal spacetime Dirac Lagrangian, revealing new vertices, parity violation, and restrictions on spin states, thus offering a combinatorial and geometric foundation for particle physics.

Contribution

It introduces a combinatorial derivation of standard model interactions from an internal spacetime Dirac Lagrangian, including new vertices and parity violation features.

Findings

Derivation of standard model trivalent vertices from internal Dirac Lagrangian

Identification of two new longitudinal Z vertices for four-valent boson interactions

Explanation of electroweak parity violation for leptons and quarks

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 dimension, 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 additional new (longitudinal) Z 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-2 boson predicted by the model.