Physical applications of homogeneous balls
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The work Physical applications of homogeneous balls represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Physical applications of homogeneous balls
Resource Information
The work Physical applications of homogeneous balls represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Physical applications of homogeneous balls
 Statement of responsibility
 Yaakov Friedman, with the assistance of Tzvi Scarr
 Subject

 Classical and Quantum Gravitation, Relativity Theory.
 Differential Geometry.
 Geometry.
 Global differential geometry.
 Homogeneous spaces
 Homogeneous spaces
 Homogeneous spaces
 Mathematical Methods in Physics.
 Mathematical physics  Mathematical models
 Mathematical physics  Mathematical models
 Mathematical physics  Mathematical models
 Mathematical physics.
 Special relativity (Physics)
 Special relativity (Physics)
 Special relativity (Physics)
 Topological Groups, Lie Groups.
 Topological Groups.
 Applications of Mathematics.
 Language
 eng
 Summary
 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. It is shown that the set of all possible velocities is a BSD with respect to the projective group; the Lie algebra of this group, expressed as a triple product, defines relativistic dynamics. The particular BSD known as the spin factor is exhibited in two ways: first, as a triple representation of the Canonical Anticommutation Relations, and second, as a ball of symmetric velocities. The associated group is the conformal group, and the triple product on this domain gives a representation of the geometric product defined in Clifford algebras. It is explained why the state space of a twostate quantum mechanical system is the dual space of a spin factor. Ideas from Transmission Line Theory are used to derive the explicit form of the operator Mobius transformations. 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. With its unifying approach to mathematics and physics, this work will be useful for researchers and graduate students interested in the many physical applications of bounded symmetric domains. It will also benefit a wider audience of mathematicians, physicists, and graduate students working in relativity, geometry, and Lie theory
 Cataloging source
 GW5XE
 Dewey number
 530.15/4
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QC20.7.H63
 LC item number
 F75 2005
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Progress in mathematical physics
 Series volume
 40
Context
Context of Physical applications of homogeneous ballsWork of
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