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Path Integral and Operator Methods in Real-Time Quantum Gravity
Path Integral and Operator Methods in Real-Time Quantum Gravity
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202105145
- ISBN
- 9798297683433
- DDC
- 530.1
- 저자명
- Held, Jesse.
- 서명/저자
- Path Integral and Operator Methods in Real-Time Quantum Gravity
- 발행사항
- [Sl] : University of California, Santa Barbara, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 300 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-04, Section: B.
- 주기사항
- Advisor: Marolf, Donald.
- 학위논문주기
- Thesis (Ph.D.)--University of California, Santa Barbara, 2025.
- 초록/해제
- 요약This dissertation details a collection of recent research studying aspects of real-time quantum gravity. It is divided into two parts. The first part details some work with the aim of understanding the Lorentzian gravitational path integral with a particular focus on the contribution of complex saddle points therein. Part two is concerned with the Hilbert space of quantum gravity, and the study of it via canonical quantization and by studying observables on said Hilbert space.Following a brief introduction to relevant concepts in chapter 1, chapter 2 discusses an alternative formulation of gravitational Renyi entropies, historically approximated by the action of Euclidean saddle points in the semiclassical limit, in terms of bulk quantum wavefunctions in a Lorentzian theory. It is noted that the bulk wavefunction encodes the Euclidean (or complex) Renyi geometries that would arise in any Euclidean path integral. As a result, for any given quantum state, the appropriate real-time path integral yields both Renyi entropies and associated complex saddle-point geometries that agree with Euclidean methods.Chapter 3 details a computation of the connected two-boundary partition function of a theory of gravity coupled to a massless axion using a Lorentzian gravitational path integral. Such calculations have been done in the context of Euclidean gravity and found that wormholes lead to large semiclassical contributions. It is found that such wormhole contributions are not present in the real-time computation. This is related back to the factorization problem of AdS/CFT.Chapter 4 attempts to generalize the notion of a fixed area state in a quantum theory of gravity, using a network of fixed area surfaces which lie in a common Cauchy slice of a semiclassical spacetime. Such a state is only robust to quantum fluctuations if all of the area operators defining the network mutually commute. The severity of such obstructions are probed 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. A simple 4-link network is defined for which all link-areas commute is found. However, the algebra generated by the link-areas of more general networks tends to be non-Abelian. One such non-Abelian example is associated with entanglement-wedge cross sections and may be of more general interest.Chapter 5 studies de Sitter JT gravity in the canonical formulation to illustrate constructions of Hilbert spaces in quantum gravity, which is challenging due to the Hamiltonian constraints. The key ideas include representing states as `invariants' or dual `co-invariants', defining a physical inner product by group averaging, and relating this to Klein-Gordon inner products via gauge-fixing conditions. A rich Hilbert space with positive-definite inner product is identified.
- 일반주제명
- Theoretical physics
- 일반주제명
- Quantum physics
- 일반주제명
- Physics
- 키워드
- Quantum gravity
- 키워드
- Hilbert space
- 기타저자
- University of California, Santa Barbara Physics
- 기본자료저록
- Dissertations Abstracts International. 87-04B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520260202105145
■006m o d
■007cr#unu||||||||
■020 ▼a9798297683433
■035 ▼a(MiAaPQ)AAI32241085
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530.1
■1001 ▼aHeld, Jesse.
■24510▼aPath Integral and Operator Methods in Real-Time Quantum Gravity
■260 ▼a[Sl]▼bUniversity of California, Santa Barbara▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a300 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-04, Section: B.
■500 ▼aAdvisor: Marolf, Donald.
■5021 ▼aThesis (Ph.D.)--University of California, Santa Barbara, 2025.
■520 ▼aThis dissertation details a collection of recent research studying aspects of real-time quantum gravity. It is divided into two parts. The first part details some work with the aim of understanding the Lorentzian gravitational path integral with a particular focus on the contribution of complex saddle points therein. Part two is concerned with the Hilbert space of quantum gravity, and the study of it via canonical quantization and by studying observables on said Hilbert space.Following a brief introduction to relevant concepts in chapter 1, chapter 2 discusses an alternative formulation of gravitational Renyi entropies, historically approximated by the action of Euclidean saddle points in the semiclassical limit, in terms of bulk quantum wavefunctions in a Lorentzian theory. It is noted that the bulk wavefunction encodes the Euclidean (or complex) Renyi geometries that would arise in any Euclidean path integral. As a result, for any given quantum state, the appropriate real-time path integral yields both Renyi entropies and associated complex saddle-point geometries that agree with Euclidean methods.Chapter 3 details a computation of the connected two-boundary partition function of a theory of gravity coupled to a massless axion using a Lorentzian gravitational path integral. Such calculations have been done in the context of Euclidean gravity and found that wormholes lead to large semiclassical contributions. It is found that such wormhole contributions are not present in the real-time computation. This is related back to the factorization problem of AdS/CFT.Chapter 4 attempts to generalize the notion of a fixed area state in a quantum theory of gravity, using a network of fixed area surfaces which lie in a common Cauchy slice of a semiclassical spacetime. Such a state is only robust to quantum fluctuations if all of the area operators defining the network mutually commute. The severity of such obstructions are probed 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. A simple 4-link network is defined for which all link-areas commute is found. However, the algebra generated by the link-areas of more general networks tends to be non-Abelian. One such non-Abelian example is associated with entanglement-wedge cross sections and may be of more general interest.Chapter 5 studies de Sitter JT gravity in the canonical formulation to illustrate constructions of Hilbert spaces in quantum gravity, which is challenging due to the Hamiltonian constraints. The key ideas include representing states as `invariants' or dual `co-invariants', defining a physical inner product by group averaging, and relating this to Klein-Gordon inner products via gauge-fixing conditions. A rich Hilbert space with positive-definite inner product is identified.
■590 ▼aSchool code: 0035.
■650 4▼aTheoretical physics
■650 4▼aQuantum physics
■650 4▼aPhysics
■653 ▼aQuantum gravity
■653 ▼aHilbert space
■653 ▼aEuclidean methods
■690 ▼a0753
■690 ▼a0599
■690 ▼a0605
■71020▼aUniversity of California, Santa Barbara▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g87-04B.
■790 ▼a0035
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17359604▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
