Non-Inertial Frames and Dirac Observables in Relativity

Describes global non-inertial frames in special and general relativity and provides a detailed description of mathematical methods.

Luca Lusanna (Author)

9781108480826, Cambridge University Press

Hardback, published 4 July 2019

336 pages
25.3 x 18.2 x 2.4 cm, 0.77 kg

'This book is devoted to making an extensive and very detailed study of the relationship between these topics and showing their application to relativistic particle systems, fluids and field theories in inertial and non-inertial systems. In this sense, as the author himself describes in the preface, it becomes clear that the transitions between non-inertial frames are gauge transformations, that extra variables are gauge variables, and that the measurable matter quantities are gauge invariant Dirac observables. The last part of the book (two chapters) is devoted to presenting a very thorough review of the Dirac-Bergmann theory of constrained systems … The book also includes three appendices that clarify some aspects and tools used in the exposition, a presentation of conclusions and a brief discussion on some of the main open problems among which, obviously, the quantization of fields in non-inertial frames stands out.' Narciso Roman-Roy, Mathematical Reviews/MathSciNet

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.

Subject Areas: Mathematical physics [PHU], Relativity physics [PHR], Cosmology & the universe [PGK]