Non-Inertial Frames and Dirac Observables in Relativity Cambridge Monographs on Mathematical Physics Series

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.

Preface; Part I. Special Relativity: Minkowski Space-time: 1. Galilei and Minkowski space-times; 2. Global non-inertial frames in special relativity; 3. Relativistic dynamics and the relativistic center of mass; 4. Matter in the rest-frame instant form of dynamics; Part II. General Relativity: Globally Hyperbolic Einstein Space-Times: 5. Hamiltonian gravity in Einstein space-times; 6. ADM tetrad gravity and its constraints; 7. Post-Minkowskian and post-Newtonian approximations; Part III. Dirac–Bergmann Theory of Constraints: 8. Singular Lagrangians and constraint theory; 9. Dirac observables invariant under the Hamiltonian gauge transformations generated by first-class constraints; 10. Concluding remarks and open problems; Appendix A. Canonical realizations of lie algebras, Poincare' group, Poincare' orbits and Wigner boosts; Appendix B. Grassmann variables and pseudo-classical Lagrangian; Appendix C. Relativistic perfect fluids and covariant relativistic thermo-dynamics; References; Index.

Luca Lusanna is a retired research director of the Firenze section of the National Institute for Nuclear Physics (INFN), of which he has been the President for five years. He is a fellow of the General Relativity and Gravitation Society, the Italian Physical Society, and Fellow and President of the General Relativity and Gravitation Italian Society. Since 2009, he has been the director of the Theoretical Topical Team of the ACES mission of ESA, tasked with putting an atomic clock on the International Space Station.