Unity Root Matrix Theory: A Quark Flavour Model

by Richard J. Miller

This book presents an integer-based representation of the quark flavour model using the mathematics of Unity Root Matrix Theory (URMT). As per a conventional quark representation, the quarks are given by eigenvectors to matrix operators, with commutation relations amongst these operators being those of the symmetry groups SU(2), for an up and down quark isospin representation, and SU(3), for an additional strange quark. The URMT method of lifting then extends this to a full, six-quark model, SU(6). Unlike conventional physical theory, the work originates in the world of number theory and Diophantine equations, and is based upon the invariance of an eigenvector equation to parametric variation in the unity root matrix - its elements are unity (or primitive) roots. The quark eigenvectors are Pythagorean or hyperbolic in nature, and parametrically evolve in both the time and frequency domain, whilst keeping all their inner product relations invariant, i.e. the model possesses unitary properties equivalent to the special unitary groups SU(2) to SU(6). Following previous publications on recasting physics in the world of number-theory, URMT has shown, once again, that the physical world may well be reducible to a simpler scheme that dances to the tune of the integers.

460 pages, Paperback

Published December 22, 2016

About the author

Richard J. Miller is the Alfred Newton Richards Professor of Pharmacology
Professor in Molecular Pharmacology and Biological Chemistry at Northwestern University.

Dr. Miller’s research has concerned the properties of neurotransmitters and their receptors in nerve cell function. This has included work on dopamine receptors, opiate receptors and cytokine receptors. Dr. Miller has also worked extensively on understanding the structure and function of calcium channels. The influx of calcium into neurons through these channels is important for many reasons, including the release of neurotransmitters. His laboratory has analyzed the properties of these molecules by examining their electrophysiological properties and has generated calcium channel knockout mice. Other projects in his lab aim to understand the molecular basis of neurodegenerative disease such as Alzheimer’s disease, amyotrophic lateral sclerosis (ALS or Lou Gehrig’s disease), HIV-1-related dementia and other neuropathological conditions.

Dr. Miller obtained his Ph.D. at Cambridge University. Prior to joining Northwestern, he was Assistant Professor and Professor at the University of Chicago.