Fixation of Coordinates in the Hamiltonian Theory of Gravitation

1959/05/01 by P. A. M. Dirac · 17 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Algorithm #Classical mechanics #Coordinate system #Cosmology and Gravitation Theories #Generalized coordinates #Geometry #Geophysics and Gravity Measurements #Gravitation #Hamiltonian (control theory) #Mathematics #Physics #Poisson bracket #Quantization (signal processing) #Quantum mechanics #Relativity and Gravitational Theory

paper · doi:10.1103/physrev.114.924

openalex publication_date 1959/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/03

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.

Citations

• Generalized Hamiltonian Dynamics

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