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Fixation of Coordinates in the Hamiltonian Theory of Gravitation
Abstract
The theory of gravitation is usually expressed in terms of an arbitrary system of coordinates. This results in the appearance of weak equations connecting the Hamiltonian dynamical variables that describe a state at a certain time, leading to supplementary conditions on the wave function after quantization. It is then difficult to specify the initial state in any practical problem.To remove the difficulty one must eliminate the weak equations by fixing the coordinate system. The general procedure for this elimination is here described. A particular way of fixing the coordinate system is then proposed and its effect on the Poisson bracket relations is worked out.
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Citations
Cited by
Quantum Theory of Gravity. I. The Canonical Theory
DeWitt, B. S. (1967) · Physical Review · doi:10.1103/physrev.160.1113 · Cited by 3,385
Role of Conformal Three-Geometry in the Dynamics of Gravitation
York, J. W. (1972) · Physical Review Letters · doi:10.1103/physrevlett.28.1082 · Cited by 1,392
Loop space representation of quantum general relativity
Rovelli, C., & Smolin, L. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90019-a · Cited by 806
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
Burgess, C. P. (2004) · Living Reviews in Relativity · doi:10.12942/lrr-2004-5 · Cited by 748
The Feynman integral for singular Lagrangians
Faddeev, L. D. (1969) · Theoretical and Mathematical Physics · doi:10.1007/bf01028566 · Cited by 731
Metadata
- Authors
- Dirac, P. A. M.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1959-05-01
- Volume
- 114
- Issue
- 3
- Pages
- 924-930
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2038365242
- Cited by
- 488
- References
- 0
- FWCI
- 7.78
- Type
- journal article
- Language
- en
- Open access
- closed
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- Dirac, P. A. M. (1959). Fixation of Coordinates in the Hamiltonian Theory of Gravitation. Physical Review. https://doi.org/10.1103/physrev.114.924
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