Non-inertial frames and Dirac observables in relativity / Luca Lusanna (National Institute for Nuclear Physics(INFN), Firenze).
Interpreting general relativity relies on a proper description of non-inertial frames and Dirac observables. This book describes global non-inertial frames in special and general relativity. The first part covers special relativity and Minkowski space time, before covering general relativity, global...
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| Format: | eBook |
| Language: | English |
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Cambridge, United Kingdom ; New York, NY :
Cambridge University Press,
2019.
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| Series: | Cambridge monographs on mathematical physics.
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Table of Contents:
- Cover; Half-title; Series information; Title page; Copyright information; Dedication; Contents; Preface; Part I Special Relativity: Minkowski Space-Time; 1 Galilei and Minkowski Space-Times; 1.1 The Galilei Space-Time of Non-Relativistic Physics and Its Inertial and Non-Inertial Frames; 1.2 The Minkowski Space-Time: Inertial Frames, Cartesian Coordinates, Matter, Energy-Momentum Tensor, and Poincaré Generators; 1.3 The 1+3 Approach to Local Non-Inertial Frames and Its Limitations; 2 Global Non-Inertial Frames in Special Relativity
- 2.1 The 3+1 Approach to Global Non-Inertial Frames and Radar 4-Coordinates2.2 Parametrized Minkowski Theory for Matter Admitting a Lagrangian Description; 3 Relativistic Dynamics and the Relativistic Center of Mass; 3.1 The Wigner-Covariant Rest-Frame Instant Form of Dynamics for Isolated Systems; 3.2 The Relativistic Center-of-Mass Problem; 3.3 The Elimination of Relative Times in Relativistic Systems of Particles and in Relativistic Bound States; 3.4 Wigner-Covariant Quantum Mechanics of Point Particles; 3.5 The Non-Inertial Rest-Frames; 4 Matter in the Rest-Frame Instant Form of Dynamics
- 4.1 The Klein-Gordon Field4.2 The Electromagnetic Field and Its Dirac Observables; 4.3 Relativistic Atomic Physics; 4.4 The Dirac Field; 4.5 Yang-Mills Fields; 4.6 Relativistic Fluids, Relativistic Micro-Canonical Ensemble, and Steps toward Relativistic Statistical Mechanics; 4.6.1 The Relativistic Perfect Fluid; 4.6.2 The Relativistic Micro-Canonical Ensemble; 4.6.3 Steps towards Relativistic Statistical Mechanics; Part II General Relativity: Globally Hyperbolic Einstein Space-Times; 5 Hamiltonian Gravity in Einstein Space-Times
- 5.1 Global 3+1 Splittings of Globally Hyperbolic Space-Times without Super-Translations and Asymptotically Minkowskian at Spatial Infinity Admitting a Hamiltonian Formulationof Gravity5.2 The ADM Hamiltonian Formulation of Einstein Gravity and the Asymptotic ADM Poincaré Generators in the Non-Inertial Rest-Frames; 6 ADM Tetrad Gravity and Its Constraints; 6.1 ADM Tetrad Gravity, Its Hamiltonian Formulation, and Its First-Class Constraints; 6.2 The Shanmugadhasan Canonical Transformation to the York Canonical Basis for the Search of the Dirac Observables of the Gravitational Field
- 6.3 The Non-Harmonic 3-Orthogonal Schwinger Time Gauges and the Metrological Interpretation of the Inertial Gauge Variables6.4 Point Particles and the Electromagnetic Field as Matter; 7 Post-Minkowskian and Post-Newtonian Approximations; 7.1 The Post-Minkowskian Approximation in the 3-Orthogonal Gauges; 7.2 The Post-Newtonian Expansion of the Post-Minkowskian Linearization; 7.3 Dark Matter as a Relativistic Inertial Effect and Relativistic Celestial Metrology; 7.3.1 Masses of Clusters of Galaxies from the Virial Theorem