1999/10/21 by Yoshiaki Ohkuwa, Ohkuwa, Yoshiaki
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Quantum Information and Cryptography #Quantum Mechanics and Applications #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9910071
19 pages, Latex, 1 figure
openalex publication_date 1999/10/21 · arxiv created 1999/10/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In order to study the "problem of time", 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'. 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.