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Canonical Variables for General Relativity

1960; American Institute of Physics; Volume: 117; Issue: 6 Linguagem: Inglês

10.1103/physrev.117.1595

1536-6065

R. Arnowitt, S. Deser, Charles W. Misner,

Black Holes and Theoretical Physics

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.