Quantum number conservation: a tool in the design and analysis of high energy experiments

Abstract

The Clifford Unification algebra $C{l}_{7,7}$ is shown to provide a unified description of all the elementary fermions and hadrons in terms of seven binary quantum numbers. Four of these are defined in existing theories, namely spin-direction, fermion/anti-fermion pairing and the two commuting generators in the SU(3) description of quark colour. A $C{l}_{3,3}$ sub-algebra integrates the $C{l}_{1,3}$ space-time and Dirac algebras providing a new definition of time direction and identifying parity as a new quantum number. A further two quantum numbers are related to the commuting generators of an SU(3) description of fermion generations. All seven are conserved in the decays and interactions of charged particles, suggesting that quantum number conservation provides a useful tool in the design and interpretation of high energy experiments. This is especially relevant when neutral particles and parity are involved.

arXiv comment17 pages

References in corpus (10)

• Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra
• A geometric basis for the standard-model gauge group
• The Standard Model Algebra - Leptons, Quarks, and Gauge from the Complex Clifford Algebra Cl6
• Majorana Neutrinos, Exceptional Jordan Algebra, and Mass Ratios for Charged Fermions
• The Unified Standard Model
• A Geometric Approach to the Standard Model
• Clifford Algebras, Spinors and $Cl(8,8)$ Unification
• Fourth Generation fermions as candidates for Dark Matter
• Repairing the algebraic foundations of the Standard Model of particle physics
• Quantum number conservation in intergenerational interactions