Coherent state approach to quantum clocks

The {open_quotes}problem of time{close_quotes} has been a pressing issue in quantum gravity for some time. To help understand this problem, Rovelli proposed a model of a two harmonic oscillator system where one of the oscillators can be thought of as a {open_quotes}clock{close_quotes} for the other oscillator, thus giving a natural time reference frame for the system. Recently, the author has constructed an explicit form for coherent states on the reduced phase space of this system in terms of Klauder{close_quote}s projection operator approach. In this paper, I will discuss the features of this model, and then by using coherent state representations and other tools from coherent state quantization, I investigate the construction of gauge-invariant operators on this reduced phase space and the ability to use a quantum oscillator as a {open_quotes}clock.{close_quotes} {copyright} {ital 1998} {ital The American Physical Society}