Background independent duals of the harmonic oscillator.
We show that a class of topological field theories are quantum duals of the harmonic oscillator. This is demonstrated by establishing a correspondence between the creation and annihilation operators and nonlocal gauge invariant observables of the topological field theory. The example is used to discuss some issues concerning background independence and the relation of vacuum energy to the problem of time in quantum gravity.
Husain
Viqar
V
Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo ON, Canada N2L 2Y5. vhusain@perimeterinstitute.ca