UID:
almafu_9961000628002883
Umfang:
1 online resource (223 pages)
ISBN:
3-031-16045-2
Serie:
Synthesis lectures on mathematics & statistics
Anmerkung:
Includes index.
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Intro -- Preface -- Contents -- Acronyms -- Part I De Sitterian Elementary Systems -- 1 Introduction -- [DELETE] -- 1.1 Brief Description -- 1.2 Motivations -- 1.3 Content at a Glance -- 1.4 Reading Guide and Conventions -- Part II As a Preliminary: 1 + 1-Dimensional dS (dS2) Geometry and Relativity -- 2 The Classical Context -- [DELETE] -- 2.1 DS2 Manifold and Its Symmetry Group -- 2.1.1 Precision on SO0(1,2): A Geometric Viewpoint -- 2.1.2 Homomorphism Between SO0(1,2) and SU(1,1) -- 2.2 Relativistic Meaning of the dS2 Group: Group Decomposition -- 2.2.1 Space-Time-Lorentz Decomposition -- 2.2.2 Cartan Decomposition -- 2.2.3 Iwasawa Decomposition -- 2.3 DS2 Lie Algebra and Classical Phase Spaces -- 2.3.1 Co-adjoint Orbits: A Brief Introduction -- 2.3.2 DS2 (co-)Adjoint Orbits as Possible Phase Spaces for Motions on dS2 Spacetime -- 3 The Quantum-Mechanical Context -- [DELETE] -- 3.1 UIR's of the dS2 Group and Quantum Version of dS2 Motions -- 3.2 UIR's of the dS2 Group: Global Realization -- 3.2.1 Group Representations: A Brief Introduction -- 3.2.2 Principal Series -- 3.2.3 Complementary Series -- 3.2.4 Discrete Series -- Part III 1 + 3-Dimensional dS (dS4) Geometry and Relativity -- 4 The Classical Context -- [DELETE] -- 4.1 DS4 Manifold and Its Causal Structure -- 4.2 DS4 Relativity Group SO0(1,4) and Its Covering Sp(2,2) -- 4.2.1 Homomorphism Between SO0(1,4) and Sp(2,2) and Some Discrete Symmetries -- 4.3 Relativistic Meaning of the dS4 Group: Group Decomposition -- 4.3.1 Space-Time-Lorentz Decomposition -- 4.3.2 Cartan Decomposition -- 4.3.3 Iwasawa Decomposition -- 4.3.4 Four Integration Formulas on Sp(2,2) -- 4.4 Relativistic Meaning of the dS4 Group: Group (Algebra) Contraction -- 4.4.1 Group (Algebra) Contraction: A Brief Introduction -- 4.4.2 DS4 Group (Algebra) Contractions -- 4.5 DS4 Lie Algebra and Classical Phase Spaces.
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4.5.1 Phase Space for Scalar ``Massive''/``Massless'' Elementary Systems in dS4 Spacetime -- 4.5.2 Phase Space for ``Spin''``Massive'' Elementary Systems in dS4 Spacetime -- 4.5.3 Phase Space for ``Spin'' (or Helicity) ``Massless'' Elementary Systems in dS4 Spacetime -- 5 The Quantum-Mechanical Context -- [DELETE] -- 5.1 UIR's of the dS4 Group and Quantum Version of dS4 Motions -- 5.1.1 Discrete Series -- 5.1.2 Principal Series -- 5.1.3 Complementary Series -- 5.1.4 Discussion: A Natural Fuzzyness of dS4 Spacetime -- 5.2 UIR's of the dS4 Group: Global Realization -- 5.2.1 Principal Series: Scalar Case -- 5.2.2 Principal Series: General Case -- 5.2.3 Principal Series: Restriction to the Maximal Compact Subgroup SU(2) timesSU(2) -- 5.2.4 Complementary Series -- 5.2.5 Discrete Series -- 5.3 ``Massive''/``Massless'' dS4 UIR's and the Poincaré Contraction -- 5.3.1 Group Contraction (The Representation Level): A Brief Introduction -- 5.3.2 DS4 Massive UIR's -- 5.3.3 DS4 Massless UIR's -- 5.3.4 Discussion: Rehabilitating the dS4 Physics from the Point of View of a Local Minkowskian Observer -- 5.3.5 For Comparison: AdS4 UIR's and the Poincaré Contraction -- 6 The QFT Context -- [DELETE] -- 6.1 An Overview -- 6.2 DS4 Wave Equations -- 6.2.1 Computation in Ambient Notations -- 6.2.2 Link to Intrinsic Coordinates -- 6.3 Plane-Wave Type Solutions -- 6.3.1 A Global Definition: dS4 Plane Waves in Their Tube Domains -- 6.3.2 Precision on Orbital Basis of the Cone -- 6.3.3 DS4 Plane Waves as Generating Functions for Square-Integrable Eigenfunctions -- 6.3.4 DS4 Plane Waves and the Zero-Curvature Limit -- 6.4 QFT in dS4 Spacetime -- 6.4.1 Local dS4 Scalar Fields: Generalized Free Fields -- 6.4.2 (Analytic) Wightman Two-Point Functions for the dS4 (Principal and Complementary) Klein-Gordon Scalar Fields.
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6.4.3 Minimally Coupled Scalar Field as an Illustration of a Krein Structure -- 7 Notion of Mass in (A)dS4 Relativity -- [DELETE] -- 7.1 An Overview -- 7.2 Discussion/Reminder: Mass and Symmetries -- 7.3 Garidi Mass: Definition -- 7.4 Garidi Mass: A More Elaborate Discussion -- 7.4.1 DS4 Case -- 7.4.2 AdS4 Case -- 7.4.3 Discussion: Dark Matter as a Relic AdS4 Curvature Energy (?) -- 7.5 Garidi Mass: Examples and Applications -- 7.5.1 ``Partially Massless'' Fields -- 7.5.2 The Question of Graviton ``Mass'' -- Index -- Index.
Weitere Ausg.:
Print version: Enayati, Mohammad The de Sitter (dS) Group and Its Representations Cham : Springer International Publishing AG,c2023 ISBN 9783031160448
Sprache:
Englisch
