A wave equation including leptons and quarks for the standard model of quantum physics in Clifford Algebra

TL;DR

This paper introduces a Clifford algebra-based wave equation that unifies leptons and quarks within the standard model, maintaining gauge and relativistic invariance in an extended geometric framework.

Contribution

It presents a novel wave equation in Clifford algebra that incorporates all first-generation particles and symmetries of the standard model, extending the geometric understanding of particle physics.

Findings

Wave equation is gauge invariant under standard model groups.

Equation is form invariant under a generalized relativistic group.

All standard model features are linked to extended space-time geometry.

Abstract

A wave equation with mass term is studied for all particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks $u$ and $d$ with three states of color and antiquarks $\overline{u}$ and $\overline{d}$. This wave equation is form invariant under the $Cl_3^*$ group generalizing the relativistic invariance. It is gauge invariant under the $U(1)\times SU(2) \times SU(3)$ group of the standard model of quantum physics. The wave is a function of space and time with value in the Clifford algebra $Cl_{1,5}$. All features of the standard model, charge conjugation, color, left waves, Lagrangian formalism, are linked to the geometry of this extended space-time.