Non-Inertial Frames and Dirac Observables in Relativity

2019/06/17 by Luca Lusanna · 1 voice
Physics and Astronomy · #Relativity and Gravitational Theory #Cosmology and Gravitation Theories #Quantum Mechanics and Applications

paper · doi:10.1017/9781108691239

openalex publication_date 2019/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

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.

Citations

• Simultaneity, radar 4-coordinates and the 3+1 point of view about accelerated observers in special relativity
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Generalized Hamiltonian Dynamics
• Gibbs ensembles in relativistic classical and quantum mechanics
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• The use of generalized functions and distributions in general relativity
• Particle spin dynamics as the grassmann variant of classical mechanics
• Relational quantum mechanics
• On the proof of the positive mass conjecture in general relativity
• Simultaneity, conventialism, general covariance, and the special theory of relativity
• Constraints in Covariant Field Theories
• Nonstationary irreversible thermodynamics: A causal relativistic theory
• A new proof of the positive energy theorem
• Decoherence, einselection, and the quantum origins of the classical
• Action functionals for relativistic perfect fluids
• Ergodic Properties of Microcanonical Observables
• The Gribov problem and QCD dynamics

Discussions

• Il est difficile, en relativité générale, de définir rigoureusement (c'-à-d indépendamment de tout système de coordonnées) la 'platitude asymptotique' d'un espace-temps courbe (et, par conséquent, de [bsky, 2 points, 0 comments]

Related

• Dirac-Bergmann Constraints in Relativistic Physics: Non-Inertial Frames,\n Point Particles, Fields and Gravity
• Non-Inertial Frames in Special and General Relativity
• The York Map and the Role of Non-Inertial Frames in the Geometrical View of the Gravitational Field
• The Chrono'Geometrical Structure of Special and General Relativity: Towards a Background-Independent Description of the Gravitational Field and Elementary Particles
• Inertial frames of reference, space and time measurements, and physical principles of special relativity revisited