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Mathematics of the Holographic Principle
Mathematics of the Holographic Principle
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202105058
- ISBN
- 9798288818318
- DDC
- 530
- 서명/저자
- Mathematics of the Holographic Principle
- 발행사항
- [Sl] : California Institute of Technology, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 606 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
- 주기사항
- Advisor: Marcolli, Matilde.
- 학위논문주기
- Thesis (Ph.D.)--California Institute of Technology, 2025.
- 초록/해제
- 요약The holographic principle, which states that quantum gravity in a given spacetime region admits an equivalent description in terms of a quantum system without gravity on its boundary, is a very promising candidate to lay the foundations of our understanding of quantum gravity. However, a precise general formulation of this principle, as well as its domain of applicability, are yet to be understood. This thesis explores the foundations of holography from a mathematical point of view. In particular, the theory of von Neumann algebras is exploited to understand features of the emergence of spacetime in holography, leveraging tools from quantum error correction in infinite dimensions as well as results on harmonic analysis. Some connections between hyperbolic geometry and recent developments in holography are also elucidated, an approach to the factorization of holographic theories based on Hopf algebras is developed, and a puzzle regarding the description of a closed universe within the context of the AdS/CFT correspondence is put forward.
- 일반주제명
- Spacetime
- 일반주제명
- Eigenvalues
- 일반주제명
- Gravity
- 일반주제명
- Black holes
- 일반주제명
- Hilbert space
- 일반주제명
- High temperature
- 일반주제명
- Quantum physics
- 일반주제명
- Theoretical physics
- 기타저자
- California Institute of Technology Physics Mathematics and Astronomy
- 기본자료저록
- Dissertations Abstracts International. 87-01B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
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■020 ▼a9798288818318
■035 ▼a(MiAaPQ)AAI32205956
■035 ▼a(MiAaPQ)Caltech17348
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530
■1001 ▼aGesteau, Elliott.▼0(orcid)0000-0002-3189-0953
■24510▼aMathematics of the Holographic Principle
■260 ▼a[Sl]▼bCalifornia Institute of Technology▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a606 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-01, Section: B.
■500 ▼aAdvisor: Marcolli, Matilde.
■5021 ▼aThesis (Ph.D.)--California Institute of Technology, 2025.
■520 ▼aThe holographic principle, which states that quantum gravity in a given spacetime region admits an equivalent description in terms of a quantum system without gravity on its boundary, is a very promising candidate to lay the foundations of our understanding of quantum gravity. However, a precise general formulation of this principle, as well as its domain of applicability, are yet to be understood. This thesis explores the foundations of holography from a mathematical point of view. In particular, the theory of von Neumann algebras is exploited to understand features of the emergence of spacetime in holography, leveraging tools from quantum error correction in infinite dimensions as well as results on harmonic analysis. Some connections between hyperbolic geometry and recent developments in holography are also elucidated, an approach to the factorization of holographic theories based on Hopf algebras is developed, and a puzzle regarding the description of a closed universe within the context of the AdS/CFT correspondence is put forward.
■590 ▼aSchool code: 0037.
■650 4▼aSpacetime
■650 4▼aEigenvalues
■650 4▼aGravity
■650 4▼aBlack holes
■650 4▼aHilbert space
■650 4▼aHigh temperature
■650 4▼aQuantum physics
■650 4▼aTheoretical physics
■690 ▼a0599
■690 ▼a0753
■71020▼aCalifornia Institute of Technology▼bPhysics, Mathematics and Astronomy.
■7730 ▼tDissertations Abstracts International▼g87-01B.
■790 ▼a0037
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17359302▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
