Overview

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.

Full Product Details

Author:   Tzvi Scarr ,  Yaakov Friedman
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 2005
Volume:   40
Dimensions:   Width: 15.50cm , Height: 1.60cm , Length: 23.50cm
Weight:   0.468kg
ISBN:  

9781461264934

ISBN 10:   1461264936
Pages:   279
Publication Date:   23 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

1 Relativity based on symmetry.- 1.1 Space-time transformation based on relativity.- 1.2 Step 6 - Identification of invariants.- 1.3 Relativistic velocity addition.- 1.4 Step 7 - The velocity ball as a bounded symmetric domain.- 1.5 Step 8 - Relativistic dynamics.- 1.6 Notes.- 2 The real spin domain.- 2.1 Symmetric velocity addition.- 2.2 Projective and conformal commutativity and associativity.- 2.3 The Lie group Aut,(Ds) 64 2.3.1 The automorphisms of Ds generated by s-velocity addition.- 2.4 The Lie Algebra autc(Ds) and the spin triple product.- 2.5 Relativistic dynamic equations on Ds.- 2.6 Perpendicular electric and magnetic fields.- 2.7 Notes.- 3 The complex spin factor and applications.- 3.1 The algebraic structure of the complex spin factor.- 3.2 Geometry of the spin factor.- 3.3 The dual space of Sn.- 3.4 The unit ball Ds,n of Sn as a bounded symmetric domain.- 3.5 The Lorentz group representations on Sn.- 3.6 Spin-2 representation in dinv (84).- 3.7 Summary of the representations of the Lorentz group on S3 and S4.- 3.8 Notes.- 4 The classical bounded symmetric domains.- 4.1 The classical domains and operators between Hilbert spaces.- 4.2 Classical domains are BSDs.- 4.3 Peirce decomposition in JC*-triples.- 4.4 Non-commutative perturbation.- 4.5 The dual space to a JC*-triple.- 4.6 The infinite-dimensional classical domains.- 4.7 Notes.- 5 The algebraic structure of homogeneous balls.- 5.1 Analytic mappings on Banach spaces.- 5.2 The group Auta (D).- 5.3 The Lie Algebra of Auta(D).- 5.4 Algebraic properties of the triple product.- 5.5 Bounded symmetric domains and JB*-triples.- 5.6 The dual of a JB*-triple.- 5.7 Facially symmetric spaces.- 5.8 Notes.- 6 Classification of JBW*-triple factors.- 6.1 Building blocks of atomic JBW*-triples.- 6.2 Methods of gluing quadrangles.- 6.3 Classification of JBW*-triple factors.- 6.4 Structure and representation of JB*-triples.- 6.5 Notes.- References.

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)

"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)"

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