Fixation of Coordinates in the Hamiltonian Theory of Gravitation

P. A. M. Dirac
Phys. Rev. 114, 924 – Published 1 May 1959
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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.

  • Received 10 December 1958

DOI:https://doi.org/10.1103/PhysRev.114.924

©1959 American Physical Society

Authors & Affiliations

P. A. M. Dirac*

  • Institute for Advanced Study, Princeton, New Jersey

  • *The author's stay at the Institute for Advanced Study was supported by the National Science Foundation.

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Issue

Vol. 114, Iss. 3 — May 1959

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