Coherent state approach to quantum clocks

The “problem of time” 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 “clock” 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’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 “clock.”