Publications

Detailed Information

Quantum point particle approximation of spinning black holes and compact stars : 회전하는 블랙홀과 밀집성의 양자 점입자 근사

DC Field Value Language
dc.contributor.advisor이상민-
dc.contributor.author김정욱-
dc.date.accessioned2020-10-13T03:59:43Z-
dc.date.available2020-10-13T03:59:43Z-
dc.date.issued2020-
dc.identifier.other000000162347-
dc.identifier.urihttps://hdl.handle.net/10371/170669-
dc.identifier.urihttp://dcollection.snu.ac.kr/common/orgView/000000162347ko_KR
dc.description학위논문 (박사) -- 서울대학교 대학원 : 자연과학대학 물리학과, 2020. 8. 이상민.-
dc.description.abstractGravitational wave observatories targeted for compact binary coalescence, such as LIGO and VIRGO, require various theoretical inputs for their efficient detection. One of such inputs are analytical description of binary dynamics at sufficiently separated orbital scales, commonly known as post-Newtonian dynamics. One approach for determining such two-body effective Hamiltonians is to use quantum scattering amplitudes.

This dissertation aims at an improved understanding of classical physics of spinning bodies in quantum scattering amplitudes, for application to the problem of effective two-body Hamiltonians. The main focus will be on spin-induced higher-order multipole moments. In this dissertation results for the first post-Minkowskian order (linear in Newton's constant G and to all orders in relative momentum p^2) Hamiltonian that is valid for arbitrary compact spinning bodies to all orders in spin is presented. Next, obstruction and prospects for the formulation's extension to second post-Minkowskian order is discussed, based on an equivalent loop order quantum field theory computations.

This dissertation is based on the works [1-4]
-
dc.description.abstractLIGO나 VIRGO와 같이 밀집쌍성계(compact binary coalescence)를 주요 중력파원으로 삼는 중력파 검출기에서는 효과적인 중력파 검출을 위해 다양한 이론적 도구를 필요로 한다. 그러한 이론적 도구 중 하나는 충분한 거리를 두고 공전하고 있는 쌍성계의 동역학에 대한 해석적 묘사로, 포스트-뉴턴 전개(post-Newtonian expansion)란 이름으로 널리 알려져 있다. 이러한 이체 문제의 유효 해밀토니안을 구하는 방법 중 하나는 양자역학적 산란진폭을 이용하는 것이다.

이 학위논문은 이체 문제의 유효 해밀토니안을 구하는 문제에 응용될 수 있도록 양자역학적 산란진폭에 포함된 회전하는 물체의 고전물리 중 스핀에 의해 생성된 고차 다중극(multipole moment) 효과의 이해를 목표로 한다. 이 논문에서는 임의의 회전하는 밀집성에 대해 스핀의 모든 차수 효과를 고려한 일차 포스트-민코프스키 전개 (뉴턴상수 G에 대해 선형이며 상대운동량 p^2에 대해 모든 차수를 포함) 유효 해밀토니안을 제시한다. 다음으로 이 방법론을 이차 포스트-민코프스키 전개로 확장할 때의 장애와 전망에 대해 동등한 차수의 양자장론 계산을 통해 논한다.

이 학위논문은 [1-4]의 논문을 바탕으로 한다.
-
dc.description.tableofcontentsChapter 1 Introduction 1
Chapter 2 Preliminaries 6
2.1 Effective field theory for binary dynamics 6
2.1.1 Overview of effective field theory for gravitational radiation from stellar binaries 6
2.1.2 The point particle effective action 9
2.2 Analyticity properties of the S-matrix 11
2.2.1 Simple poles and one-particle states 12
2.2.2 The optical theorem and Cutkosky rules 15
2.2.3 Generalised unitarity and scalar integral coefficients 17
2.3 The on-shell formalism for the S-matrix 21
2.3.1 The spinor-helicity formalism 22
2.3.2 Spinor-helicity for massive particles 23
2.3.3 Little group constraints of amplitudes 25
2.3.4 Kinematical constraints for three-point amplitudes 26
2.4 Two-body effective Hamiltonians from quantum scattering amplitudes 28
2.4.1 Classification of perturbative general relativity 28
2.4.2 Mapping amplitudes to effective Hamiltonians 29
2.4.3 The classical limit of finite spin particles 31
Chapter 3 Applications at tree level 34
3.1 The gravitational three-point amplitude 34
3.1.1 Amplitudes from point particle effective action 34
3.1.2 Hilbert space matching 37
3.1.3 The residue integral representation 44
3.2 Constructing the 1PM Hamiltonian from amplitudes 46
3.2.1 Kinematics for 1PM computation 46
3.2.2 1PM amplitude 48
3.2.3 Thomas-Wigner rotation 50
3.2.4 Complete 1PM potential 53
3.3 1PM potential at each spin order 54
3.3.1 Linear in spin 56
3.3.2 Quadratic in spin 57
3.3.3 Cubic in spin 58
3.3.4 Quartic in spin 59
3.4 Reproducing 1PM part of PN expansion 61
3.4.1 Linear in spin (up to NNNLO) 62
3.4.2 Quadratic in spin (up to NNLO) 65
Chapter 4 Obstructions and applications at one-loop level 73
4.1 The gravitational Compton amplitude 73
4.1.1 The naive gravitational Compton amplitude 73
4.1.2 Resolving the spurious pole of naive Compton amplitude 75
4.2 Matter stress tensor for Kerr-Newman black holes 77
4.2.1 Classical computations in Kerr-Schild coordinates 78
4.2.2 Quantum field theory computations 83
4.3 One-loop amplitude for 2PM spinning BH Hamiltonian at HCL 95
4.3.1 Kinematical set-up 97
4.3.2 The box integral contribution at HCL 99
4.3.3 The triangle integral contribution at HCL 100
4.4 Discussions and outlook for one-loop order 102
Chapter A Conventions 104
A.1 Invariant tensors 104
A.2 Analytic continuation and complex conjugation 105
A.3 Numerical implementations and the high-energy limit 106
A.4 Dirac spinors 108
A.5 Polarisation vectors 108
A.6 BOLD notation 109
초록 126
감사의 글 127
-
dc.language.isoeng-
dc.publisher서울대학교 대학원-
dc.subjectScattering amplitudes-
dc.subjectPost-Newtonian expansion-
dc.subjectPost-Minkowskian expansion-
dc.subject산란진폭-
dc.subject포스트-뉴턴 전개-
dc.subject포스트-민코프스키 전개-
dc.subject.ddc530-
dc.titleQuantum point particle approximation of spinning black holes and compact stars-
dc.title.alternative회전하는 블랙홀과 밀집성의 양자 점입자 근사-
dc.typeThesis-
dc.typeDissertation-
dc.contributor.AlternativeAuthorJung-Wook Kim-
dc.contributor.department자연과학대학 물리학과-
dc.description.degreeDoctor-
dc.date.awarded2020-08-
dc.contributor.major이론물리학-
dc.identifier.uciI804:11032-000000162347-
dc.identifier.holdings000000000043▲000000000048▲000000162347▲-
Appears in Collections:
Files in This Item:

Altmetrics

Item View & Download Count

  • mendeley

Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.

Share