Overview
- Develops new tools to efficiently describe different branches of physics within one mathematical framework
- Gives a clear geometric expression of the symmetry of physical laws
- Useful for researchers and graduate students interested in the many physical applications of bounded symmetric domains
- Will also benefit a wider audience of mathematicians, physicists, and graduate students working in relativity, geometry, and Lie theory
Part of the book series: Progress in Mathematical Physics (PMP, volume 40)
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Table of contents (6 chapters)
Keywords
About this book
One of the mathematical challenges of modern physics lies in the development of new tools to efficiently describe different branches of physics within one mathematical framework. This text introduces precisely such a broad mathematical model, one that gives a clear geometric expression of the symmetry of physical laws and is entirely determined by that symmetry.
The first three chapters discuss the occurrence of bounded symmetric domains (BSDs) or homogeneous balls and their algebraic structure in physics. The book further provides a discussion of how to obtain a triple algebraic structure associated to an arbitrary BSD; the relation between the geometry of the domain and the algebraic structure is explored as well. The last chapter contains a classification of BSDs revealing the connection between the classical and the exceptional domains.
Reviews
From the reviews:
"The aim of this book is to present the theory of Jordan algebraic structures (Jordan triple systems) and their geometric counterpart, the so-called homogeneous balls, from the point of view of applications ot mathematical physics: special relativity, spinors and foundational quantum mechanics...The (senior) author has made important research contributions to all three areas described above, and the exposition of the theory and the applications is very careful. This makes the book suitable both for experts and non-experts interested in the applications." ---Mathematical Reviews
“This fine book provides a highly original approach to theoretical physics, its contents reflecting the author’s and his ollaborators’ copious contributions to many branches of mathematics and physics over the past years.”(ZENTRALBLATT MATH)
Authors and Affiliations
Bibliographic Information
Book Title: Physical Applications of Homogeneous Balls
Authors: Yaakov Friedman, Tzvi Scarr
Series Title: Progress in Mathematical Physics
DOI: https://doi.org/10.1007/978-0-8176-8208-8
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2005
Hardcover ISBN: 978-0-8176-3339-4Published: 01 December 2004
Softcover ISBN: 978-1-4612-6493-4Published: 23 October 2012
eBook ISBN: 978-0-8176-8208-8Published: 08 January 2013
Series ISSN: 1544-9998
Series E-ISSN: 2197-1846
Edition Number: 1
Number of Pages: XXIII, 279
Topics: Applications of Mathematics, Mathematical Methods in Physics, Geometry, Classical and Quantum Gravitation, Relativity Theory, Topological Groups, Lie Groups, Differential Geometry