Discrete symmetries and quantum number conservation

TL;DR

This paper explores how discrete space-time symmetries relate to fermion quantum numbers within a Clifford algebra framework, demonstrating conservation laws and implications for high-energy physics experiments.

Contribution

It introduces a novel algebraic approach linking discrete symmetries to fermion quantum numbers using Clifford algebras, refining conservation laws for high-energy physics.

Findings

Fermion quantum numbers are associated with a $Cl_{3,3}$ sub-algebra.

All seven binary quantum numbers are conserved in fermion decays and interactions.

The conservation law is modified to account for distinct F,G quantum numbers in different fermion states.

Abstract

The algebraic formulation of discrete $P$ and $T$ space-time symmetries is related to fermion quantum numbers defined by a $Cl_{3,3}$ sub-algebra of the $Cl_{7,7}$ Clifford Unification algebra. Fermion decays and interactions have been shown to conserve all seven binary quantum numbers defined by $Cl_{7,7}$. The previously formulated {\it Conservation Law} is modified to include the effects of employing distinct F,G quantum numbers in descriptions of fermions with C=+1 and C=$-1$. This is relevant in interpreting the results of high energy experiments.