The Family Problem: New Internal Algebraic and Geometric Regularities (Monographs in physics)
by Gerald L. Fitzpatrick
Category: Fermions

This book on elementary-particle physics presents a new global or "macroscopic" description of fundamental fermions (quarks & leptons). By an appropriate mathematical generalization of the concept of scalar fermion-numbers (i.e., replace the number f by a 2 by 2 matrix F, where f & F are both square-roots of unity) one arrives at a new organizing principle for fundamental fermions. Using this principle, it is possible to describe individual flavors, flavor doublets & families, of fundamental fermions, in the context of a new internal, non-Euclidean (i.e., "Lorentzian") 2-space. Certain algebraic & geometric properties of this 2-space automatically explain family replication & the number (three) of families observed in nature. Moreover, with respect to the internal transformation F, the e-type (mu- or tau-type) neutrino is found to have the same topology as a cylinder (Mobius strip). Assuming that a change in topology during neutrino-neutrino transitions is suppressed (e.g., a doughnut cannot be continuously deformed into a sphere), it is easy to calculate a matrix describing long-distance neutrino mixtures (see aps1999feb12_001 at http://publish.aps.org/eprint). See an expanded synopsis, customer reviews, comments by 1995 physics Nobel-Prize winner Martin Perl, & a Table of Contents at http;//www.amazon.com/exec/obidos/ISBN=0965569500, where the book may also be purchased.