The Resource Physical applications of homogeneous balls, Yaakov Friedman, with the assistance of Tzvi Scarr
Physical applications of homogeneous balls, Yaakov Friedman, with the assistance of Tzvi Scarr
Resource Information
The item Physical applications of homogeneous balls, Yaakov Friedman, with the assistance of Tzvi Scarr represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Physical applications of homogeneous balls, Yaakov Friedman, with the assistance of Tzvi Scarr represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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
 Language
 eng
 Extent
 1 online resource
 Contents

 Relativity based on symmetry
 The real spin domain
 The complex spin factor and applications
 The classical bounded symmetric domains
 The algebraic structure of homogeneous balls
 Classification of JBW *triple factors
 Isbn
 9780817633394
 Label
 Physical applications of homogeneous balls
 Title
 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
 http://library.link/vocab/creatorDate
 1948
 http://library.link/vocab/creatorName
 Friedman, Yaakov
 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
 http://library.link/vocab/relatedWorkOrContributorName
 Scarr, Tzvi
 Series statement
 Progress in mathematical physics
 Series volume
 40
 http://library.link/vocab/subjectName

 Homogeneous spaces
 Mathematical physics
 Special relativity (Physics)
 Homogeneous spaces
 Mathematical physics
 Special relativity (Physics)
 Label
 Physical applications of homogeneous balls, Yaakov Friedman, with the assistance of Tzvi Scarr
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 271274) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Relativity based on symmetry
 The real spin domain
 The complex spin factor and applications
 The classical bounded symmetric domains
 The algebraic structure of homogeneous balls
 Classification of JBW *triple factors
 Control code
 821595410
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9780817633394
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9780817682088
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)821595410
 Label
 Physical applications of homogeneous balls, Yaakov Friedman, with the assistance of Tzvi Scarr
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 271274) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Relativity based on symmetry
 The real spin domain
 The complex spin factor and applications
 The classical bounded symmetric domains
 The algebraic structure of homogeneous balls
 Classification of JBW *triple factors
 Control code
 821595410
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9780817633394
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9780817682088
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)821595410
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.
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Physicalapplicationsofhomogeneousballs/mCls_mpeRfk/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Physicalapplicationsofhomogeneousballs/mCls_mpeRfk/">Physical applications of homogeneous balls, Yaakov Friedman, with the assistance of Tzvi Scarr</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>