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A composite model of the standard model particles was recently derived usingthe Dirac Lagrangian on a spacetime where time does not advance along theworldlines of fundamental dust particles, called an 'internal spacetime'. Theaim of internal spacetime geometry is to model certain quantum phenomena using(classical) degenerate spacetime metrics. For example, on an internalspacetime, tangent spaces have variable dimension, and spin wavefunctioncollapse is modeled by the projection from one tangent space to another. Inthis article we show that the combinatorial structure of the internal DiracLagrangian yields precisely the standard model trivalent vertices, togetherwith two additional new (longitudinal) Z vertices that generate the four-valentboson vertices. In particular, we are able to derive electroweak parityviolation for both leptons and quarks. We also obtain new restrictions on thepossible spin states that can occur in certain interactions. Finally, wedetermine the trivalent vertices of the new massive spin-2 boson predicted bythe model.

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