1. Generalized conformal quantum mechanics as an ideal observer in two-dimensional gravity
- Author
-
Banerjee, Archi, Kibe, Tanay, Molina, Martín, and Mukhopadhyay, Ayan
- Subjects
High Energy Physics - Theory ,General Relativity and Quantum Cosmology ,Quantum Physics - 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., Comment: 35 pages
- Published
- 2024