Generalized conformal quantum mechanics as an ideal observer in two-dimensional gravity
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917955379396608 |
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| author | Banerjee, Archi Kibe, Tanay Molina, Martín Mukhopadhyay, Ayan |
| author_facet | Banerjee, Archi Kibe, Tanay Molina, Martín Mukhopadhyay, Ayan |
| contents | 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 Schrödinger 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_15415 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized conformal quantum mechanics as an ideal observer in two-dimensional gravity Banerjee, Archi Kibe, Tanay Molina, Martín Mukhopadhyay, Ayan High Energy Physics - Theory General Relativity and Quantum Cosmology Quantum Physics 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 Schrödinger 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. |
| title | Generalized conformal quantum mechanics as an ideal observer in two-dimensional gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2409.15415 |