Grassmann Duality and the Particle Spectrum

TL;DR

This paper explores how Grassmannian duality applied to particle classification schemes can naturally generate particle generations, reduce state counts, and predict exotic particles, while also deriving a value close to the experimental weak mixing angle.

Contribution

It applies Grassmannian duality to all subgroups of the standard model gauge group, determining the full particle spectrum and making novel predictions of exotic states.

Findings

Predicts quarks with charge -4/3 and other exotic states.

Derives a weak mixing angle close to experimental value.

Reduces particle states via Grassmannian duality.

Abstract

Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing sensible Lagrangians anyhow. We apply duality to all of the subgroups within the {\em classification} group SU(3)$\times$SU(2)$_L\times$SU(2)$_R$, which encompasses the standard model gauge group, and thereby determine the full state inventory; this includes the definite prediction of quarks with charge -4/3 and other exotic states. Assuming universal gravitational coupling to the gauge fields and parity even property curvature, we also obtain $4\sin^2\theta_w = 1 - 2\alpha/3\alpha_s$ which is not far from the experimental value around the $M_Z$ mass.