Other
Scientific paper
Sep 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000phrvd..62f4008o&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 62, Issue 6, 15 September 2000, id.064008
Other
2
Canonical Quantization, Lower Dimensional Models, Minisuperspace Models
Scientific paper
In order to study the ``problem of time in quantum gravity,'' Rovelli proposed a model of a two harmonic oscillator system where one of the oscillators can be thought of as a ``clock'' for the other oscillator. In this paper we examine a model where the Hamiltonian is a difference between two harmonic oscillators, and we consider one of them which has the minus sign as a `'clock,'' since the gravitational degree of freedom has a minus sign in the Hamiltonian of quantum cosmology. Klauder's projection operator approach to generalized coherent states is used to define physical states and operators. The resolution of unity is derived in terms of a gauge invariant coordinate. We investigate the ``quantum clock'' and show that the evolution described by it is identical to the classical motion when the energy becomes large.
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