1960/03/15 by R. Arnowitt, S. Deser, Charles W. Misner · 10 citations
Physics and Astronomy · Mathematics · #Cosmology and Gravitation Theories #Relativity and Gravitational Theory #Black Holes and Theoretical Physics #Poisson bracket #Canonical coordinates #Covariant Hamiltonian field theory #General relativity #Canonical quantization #Hamiltonian (control theory) #Physics #Mathematical physics #Conservation law #Theory of relativity #Covariant transformation #Classical field theory #Classical mechanics #Mathematics #Hamiltonian system #Quantum mechanics #Quantum gravity #Lie algebra #Quantum
paper · doi:10.1103/physrev.117.1595
openalex publication_date 1960/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/17
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.