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arXiv · 2205.09147

Beyond semiclassical time

Leonardo Chataignier
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Abstract

We show that the usual Born-Oppenheimer type of approximation used in quantum gravity, in which a semiclassical time parameter emerges from a weak-coupling expansion of the Wheeler-DeWitt constraint, leads to a unitary theory at least up to the next-to-leading order in minisuperspace models. As there are no unitarity-violating terms, this settles the issue of unitarity at this order, which has been much debated in the literature. Furthermore, we also show that the conserved inner product is gauge-fixed in the sense that the measure is related to the Faddeev-Popov determinant associated with the choice of semiclassical time as a reparametrization gauge. This implies that the Born-Oppenheimer approach to the problem of time is, in fact, an instance of a relational quantum theory, in which transition amplitudes can be related to conditional probabilities.

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Leonardo Chataignier. 2022-05-18. Beyond semiclassical time. https://doi.org/10.1515/zna-2022-0106

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