Scale anomaly as the origin of time
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Publication:2376005
DOI10.1007/S10714-013-1516-YzbMATH Open1269.83028arXiv1301.6173OpenAlexW1981729483WikidataQ57757737 ScholiaQ57757737MaRDI QIDQ2376005
Author name not available (Why is that?)
Publication date: 26 June 2013
Published in: (Search for Journal in Brave)
Abstract: We explore the problem of time in quantum gravity in a point-particle analogue model of scale-invariant gravity. If quantized after reduction to true degrees of freedom, it leads to a time-independent Schr"odinger equation. As with the Wheeler--DeWitt equation, time disappears, and a frozen formalism that gives a static wavefunction on the space of possible shapes of the system is obtained. However, if one follows the Dirac procedure and quantizes by imposing constraints, the potential that ensures scale invariance gives rise to a conformal anomaly, and the scale invariance is broken. A behaviour closely analogous to renormalization-group (RG) flow results. The wavefunction acquires a dependence on the scale parameter of the RG flow. We interpret this as time evolution and obtain a novel solution of the problem of time in quantum gravity. We apply the general procedure to the three-body problem, showing how to fix a natural initial value condition, introducing the notion of complexity. We recover a time-dependent Schr"odinger equation with a repulsive cosmological force in the `late-time' physics and we analyse the role of the scale invariant Planck constant. We suggest that several mechanisms presented in this model could be exploited in more general contexts.
Full work available at URL: https://arxiv.org/abs/1301.6173
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