Non-inertial frames and Dirac observables in relativity /
Lusanna, L.,
Non-inertial frames and Dirac observables in relativity / Luca Lusanna (National Institute for Nuclear Physics(INFN), Firenze). - 1 online resource. - Cambridge monographs on mathematical physics . - Cambridge monographs on mathematical physics. .
Includes bibliographical references and subject index.
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 Poincar�e 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 Poincar�e 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
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, globally hyperbolic Einstein space-time, and the application of the 3+1 splitting method to general relativity. The author uses a Hamiltonian description and the Dirac-Bergmann theory of constraints to show that the transition between one non-inertial frame and another is a gauge transformation, extra variables describing the frame are gauge variables, and the measureable matter quantities are gauge invariant Dirac observables. Point particles, fluids and fields are also discussed, including how to treat the problems of relative times in the description of relativistic bound states, and the problem of relativistic centre of mass. Providing a detailed description of mathematical methods, the book is perfect for theoretical physicists, researchers and students working in special and general relativity.
9781108575768 1108575765 9781108691239 1108691234
Dirac equation.
Wave equation.
Quantum field theory.
General relativity (Physics)
Dirac equation.
General relativity (Physics)
Quantum field theory.
Wave equation.
Electronic books.
Electronic books.
QC174.45 / .L87 2019
530.12
Non-inertial frames and Dirac observables in relativity / Luca Lusanna (National Institute for Nuclear Physics(INFN), Firenze). - 1 online resource. - Cambridge monographs on mathematical physics . - Cambridge monographs on mathematical physics. .
Includes bibliographical references and subject index.
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 Poincar�e 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 Poincar�e 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
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, globally hyperbolic Einstein space-time, and the application of the 3+1 splitting method to general relativity. The author uses a Hamiltonian description and the Dirac-Bergmann theory of constraints to show that the transition between one non-inertial frame and another is a gauge transformation, extra variables describing the frame are gauge variables, and the measureable matter quantities are gauge invariant Dirac observables. Point particles, fluids and fields are also discussed, including how to treat the problems of relative times in the description of relativistic bound states, and the problem of relativistic centre of mass. Providing a detailed description of mathematical methods, the book is perfect for theoretical physicists, researchers and students working in special and general relativity.
9781108575768 1108575765 9781108691239 1108691234
Dirac equation.
Wave equation.
Quantum field theory.
General relativity (Physics)
Dirac equation.
General relativity (Physics)
Quantum field theory.
Wave equation.
Electronic books.
Electronic books.
QC174.45 / .L87 2019
530.12