Physics
Scientific paper
Sep 1962
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1962pthph..28..529n&link_type=abstract
Progress of Theoretical Physics, Vol. 28, No. 3, pp. 529-545
Physics
7
Scientific paper
The canonical formalism of the gravitational field in the expanding universe is examined from the standpoint of the general theory of relativity. The formalism of Arnowitt-Deser-Misner is modified in order to take an expanding model of the universe as the background space-time, in place of the Minkowski space-time. It is shown that the separation of the cosmological background and the gravitational field is performed in the Lagrangian formalism without destroying compatibility with Einstein's field equation. By imposing a suitable set of coordinate conditions, two independent pairs of canonical variables of the pure gravitational field are exhibited and the Hamiltonian for them is obtained by means of the iteration method. A detailed discussion will be given for the case of linearized theory and it is shown, as the most characteristic feature of our system, that the Hamiltonian obtained is non-conservative and corresponds to that of the damped harmonic oscillators.
Kimura Tadahiko
Nariai Hidekazu
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