Unity Root Matrix Theory: Mathematical and Physical Advances

by Richard J. Miller

This book naturally follows on from Volume I, developing the mathematical foundations and physical applications of the relatively new subject known as Unity Root Matrix Theory (URMT). The mathematical advances extend URMT's new method of arbitrary vector embedding to two arbitrary vectors, in three or more dimensions, by way of a complete reformulation of URMT in terms of projection operators and exterior products. The similarity of the resulting matrix forms to those used in quaternions, rotations and electromagnetism enables URMT to extend its physical applications to angular dynamics and the electromagnetic plane wave. In particular, URMT's inherently discrete nature results in a treatment of quantised particle spin. Armed with a common mathematical formulation of physical applications as an eigenvector solution to a matrix operator, all generated in a language more recognisable to conventional mathematical physics, the path is now clear for closer future development of URMT to existing, and highly successful, physical theories.

550 pages, Paperback

First published September 19, 2014

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.