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Physical Applications of Homogeneous Balls

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 symmet...

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Bibliographic Details
Main Author: Friedman, Yaakov
Format: eBook
Language:English
Published: Boston, MA Birkhäuser Boston 2005, 2005
Edition:1st ed. 2005
Series:Progress in Mathematical Physics
Subjects:
Applied Mathematics
Mathematical Methods In Physics
Differential Geometry
Engineering Mathematics
Classical And Quantum Gravitation, Relativity Theory
Topological Groups, Lie Groups
Gravitation
Lie Groups
Topological Groups
Applications Of Mathematics
Geometry
Physics
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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

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