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Quantum Operators in Gravity: From G...

Kaplan, Molly Elizabeth,

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Quantum Operators in Gravity: From Geometric Entropies to Group-Averaged Observables /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Quantum Operators in Gravity: From Geometric Entropies to Group-Averaged Observables // Molly Elizabeth Kaplan.
Author:	Kaplan, Molly Elizabeth,
Description:	1 electronic resource (236 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-05, Section: B.
Contained By:	Dissertations Abstracts International86-05B.
Subject:	Theoretical physics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31562051
ISBN:	9798342719575

Quantum Operators in Gravity: From Geometric Entropies to Group-Averaged Observables /
Kaplan, Molly Elizabeth,

Quantum Operators in Gravity: From Geometric Entropies to Group-Averaged Observables /Molly Elizabeth Kaplan. - 1 electronic resource (236 pages)

Source: Dissertations Abstracts International, Volume: 86-05, Section: B.

In this thesis, we first study the action of Hubeny-Rangamani-Takayanagi (HRT) area operators on the covariant phase space of classical solutions in Einstein-Hilbert gravity. We find that this action is a boundary-condition-preserving kink transformation, which introduces a relative boost between the entanglement wedges on either side of the HRT-surface but preserves the asymptotically Anti-de Sitter (AdS) boundary conditions. We then perform a similar analysis for the ''geometric entropy", i.e. the bulk dual to boundary entanglement entropy, in topologically massive gravity (TMG). Here, the geometric entropy is given by the HRT-area plus an anomalous contribution. We find that the action of this geometric entropy on the covariant phase space of classical solutions agrees precisely with the action of HRT-area operators in Einstein-Hilbert gravity.In Einstein-Hilbert gravity, we show that HRT-areas do not generally commute. This poses an obstruction to constructing random tensor networks (RTNs), which are most analogous to fixed-area states of the bulk quantum gravity theory, with mutually commuting HRT-areas. We probe the severity of such obstructions in pure AdS3 Einstein-Hilbert gravity by constructing networks whose links are codimension-2 extremal-surfaces and by explicitly computing semiclassical commutators of the associated link-areas. We find a simple 4-link network for which all link-areas commute, but the algebra generated by the link-areas of more general networks tends to be non-Abelian.In the final chapter, we switch gears and explore perturbative quantum gravity around de Sitter space, where gauge-invariant observables cannot be localized and, instead, local physics can arise only through certain relational constructions. In particular, we describe a class of gauge-invariant observables which, under appropriate conditions, provide good approximations to certain algebras of local fields. Our results suggest that, near any minimal Sd in dSd+1, this approximation can be accurate only over regions in which the corresponding global time coordinate t spans an interval of order ∆t ≲ ln G−1. In contrast, however, we find that the approximation can be accurate over arbitrarily large regions of global dSd+1 so long as those regions are located far to the future or past of such a minimal Sd . This in particular includes arbitrarily large parts of any static patch.

English

ISBN: 9798342719575Subjects--Topical Terms:

2144760
Theoretical physics.
Subjects--Index Terms:

Anti-de Sitter

Quantum Operators in Gravity: From Geometric Entropies to Group-Averaged Observables /
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520 $a In this thesis, we first study the action of Hubeny-Rangamani-Takayanagi (HRT) area operators on the covariant phase space of classical solutions in Einstein-Hilbert gravity. We find that this action is a boundary-condition-preserving kink transformation, which introduces a relative boost between the entanglement wedges on either side of the HRT-surface but preserves the asymptotically Anti-de Sitter (AdS) boundary conditions. We then perform a similar analysis for the ''geometric entropy", i.e. the bulk dual to boundary entanglement entropy, in topologically massive gravity (TMG). Here, the geometric entropy is given by the HRT-area plus an anomalous contribution. We find that the action of this geometric entropy on the covariant phase space of classical solutions agrees precisely with the action of HRT-area operators in Einstein-Hilbert gravity.In Einstein-Hilbert gravity, we show that HRT-areas do not generally commute. This poses an obstruction to constructing random tensor networks (RTNs), which are most analogous to fixed-area states of the bulk quantum gravity theory, with mutually commuting HRT-areas. We probe the severity of such obstructions in pure AdS3 Einstein-Hilbert gravity by constructing networks whose links are codimension-2 extremal-surfaces and by explicitly computing semiclassical commutators of the associated link-areas. We find a simple 4-link network for which all link-areas commute, but the algebra generated by the link-areas of more general networks tends to be non-Abelian.In the final chapter, we switch gears and explore perturbative quantum gravity around de Sitter space, where gauge-invariant observables cannot be localized and, instead, local physics can arise only through certain relational constructions. In particular, we describe a class of gauge-invariant observables which, under appropriate conditions, provide good approximations to certain algebras of local fields. Our results suggest that, near any minimal Sd in dSd+1, this approximation can be accurate only over regions in which the corresponding global time coordinate t spans an interval of order ∆t ≲ ln G−1. In contrast, however, we find that the approximation can be accurate over arbitrarily large regions of global dSd+1 so long as those regions are located far to the future or past of such a minimal Sd . This in particular includes arbitrarily large parts of any static patch.
546 $a English
590 $a School code: 0035
650 4 $a Theoretical physics. $3 2144760
650 4 $a Physics. $3 516296
650 4 $a Quantum physics. $3 726746
653 $a Anti-de Sitter
653 $a Hubeny-Rangamani-Takayanagi
653 $a Topologically massive gravity
653 $a Random tensor networks
690 $a 0753
690 $a 0605
690 $a 0599
710 2 $a University of California, Santa Barbara. $b Physics. $e degree granting institution. $3 3771780
720 1 $a Marolf, Donald $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-05B.
790 $a 0035
791 $a Ph.D.
792 $a 2024
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31562051