Generalized conformal quantum mechanics as an ideal observer in two-dimensional gravity

• URL: http://arxiv.org/abs/2409.15415v1
• Date: Mon, 23 Sep 2024 18:00:01 GMT
• Title: Generalized conformal quantum mechanics as an ideal observer in two-dimensional gravity
• Authors: Archi Banerjee, Tanay Kibe, Martín Molina, Ayan Mukhopadhyay,
• Abstract summary: We obtain an action for a generalized conformal mechanics (GCM) coupled to Jackiw-Teitelboim (JT) gravity from a double scaling limit of the motion of a charged massive particle. We construct the semi-classical Hilbert space of the full theory by explicitly solving the general time-dependent normalizable solutions of the Schr"odinger equation for GCM. Since the full theory of the GCM coupled to JT gravity is amenable to quantization, it can lead to a solvable model for a detector coupled to quantum gravity.
• Score: 2.380388040384068
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We obtain an action for a generalized conformal mechanics (GCM) coupled to Jackiw-Teitelboim (JT) gravity from a double scaling limit of the motion of a charged massive particle in the near-horizon geometry of a near-extremal spherical black hole. When JT gravity is treated in the classical approximation, the backreaction of the particle's wavefunction on the time-reparametrization mode (and therefore the bulk metric) vanishes while the conformal symmetry in GCM is reparametrized in a state-dependent way. We also construct the semi-classical Hilbert space of the full theory by explicitly solving the general time-dependent normalizable solutions of the Schr\"{o}dinger equation for GCM, and show that the time-reparametrization mode can be inferred from the measurement of suitable observables. Since the full theory of the GCM coupled to JT gravity is amenable to quantization, it can lead to a solvable model for a detector coupled to quantum gravity.

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