Background independent duals of the harmonic oscillator

TL;DR

This paper demonstrates a class of topological field theories as quantum duals of the harmonic oscillator, linking gauge invariants to quantum operators and exploring implications for background independence and quantum gravity.

Contribution

It introduces a novel duality between topological field theories and the harmonic oscillator, highlighting background independence in quantum gravity contexts.

Findings

Establishes a correspondence between creation/annihilation operators and gauge invariants.

Shows topological theories as duals to harmonic oscillators.

Discusses implications for vacuum energy and the problem of time.

Abstract

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 non-local 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.