Beyond semiclassical time: dynamics in quantum cosmology
- URL: http://arxiv.org/abs/2302.07903v1
- Date: Wed, 15 Feb 2023 19:00:09 GMT
- Title: Beyond semiclassical time: dynamics in quantum cosmology
- Authors: Leonardo Chataignier
- Abstract summary: We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance.
We discuss in which sense both approaches exhibit an inner product that is gauge-fixed via an operator version of the usual Faddeev-Popov procedure.
We note that a conditional probability interpretation of the physical states is possible, so that both formalisms are examples of quantum mechanics with a relational dynamics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We review two approaches to the definition of the Hilbert space and evolution
in mechanical theories with local time-reparametrization invariance, which are
often used as toy models of quantum gravity. The first approach is based on the
definition of invariant relational observables, whereas the second formalism
consists of a perturbative construction of the Hilbert space and a
weak-coupling expansion of the Hamiltonian constraint, which is frequently
performed as part of the Born-Oppenheimer treatment in quantum cosmology. We
discuss in which sense both approaches exhibit an inner product that is
gauge-fixed via an operator version of the usual Faddeev-Popov procedure, and,
in the second approach, how the unitarity of the effective Schr\"{o}dinger
evolution is established perturbatively. We note that a conditional probability
interpretation of the physical states is possible, so that both formalisms are
examples of quantum mechanics with a relational dynamics.
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