Physical Applications of Homogeneous Balls

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.