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Phys. Rev. 117, 1595–1602 (1960)

Canonical Variables for General Relativity

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R. Arnowitt*
Department of Physics, Syracuse University, Syracuse, New York

S. Deser*
Department of Physics, Brandeis University, Waltham, Massachusetts

C. W. Misner†
Universitetets Institut Teoretisk for Fysik, Copenhagen, Denmark

Received 12 October 1959; published in the issue dated March 1960

The general theory of relativity is cast into normal Hamiltonian form in terms of two pairs of independent conjugate field variables. These variables are explicitly exhibited and obey ordinary Poisson bracket relations. This form is reached by imposing a simple set of coordinate conditions. It is shown that those functionals of the metric used as invariant coordinates do not appear explicitly in the Hamiltonian and momentum densities, so that the standard differential conservation laws hold. The bearing of these results on the quantization problem is discussed.

© 1960 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRev.117.1595
DOI:
10.1103/PhysRev.117.1595
PACS:

*Supported in part by a National Science Foundation Research Grant.

†Alfred P. Sloan Research Fellow. On leave from Palmer Physical Laboratory, Princeton University, Princeton, New Jersey.

 
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