Clifford Algebras and Algebraic Structure of Fundamental Fermions

Abstract

We show, how an idea of leptons and quarks composed of algebraic partons (defined by a sequence of Clifford algebras) can explain the existence of three and only three families of these fundamental fermions. In this argument, the theory of relativity, the probability interpretation of quantum mechanics and the Pauli exclusion principle, all extended to the algebraic partons, play a crucial role. As a consequence, a semiempirical mass spectral formula for charged leptons is discussed. In terms of experimental me and m _μ , it gives successfully m _т = 1783.47 MeV or 1776.80 MeV (two options, the second fitting excellently to new measurements of m _т ).