Classical Observables from Quantum Field Theory: From Scattering Amplitudes to Binary Dynamics = 양자장론 기반 고전 관측량 연구: 산란 진폭에서 쌍성계 동역학으로

다국어 초록 (Multilingual Abstract)

This thesis explores modern scattering amplitude techniques with an emphasis on their application to classical physics. While rooted in quantum field theoretic methods, the overarching aim is to develop tools that offer new perspectives on classical dynamics.

We first study the use of Poincaré symmetry to constrain Hamiltonians in gravitational binary systems beyond the center-of-momentum frame. Next, we apply quantum off-shell recursion relations to compute cross sections in scalar field theory, focusing on learning a method that may prove useful for future classical analyses. Finally, we investigate charge-monopole scattering using partial wave expansion and the KMOC formalism, demonstrating how classical observables can be extracted in topologically nontrivial backgrounds.

Together, these studies highlight how amplitude-based techniques — ranging from symmetry principles to recursive and semiclassical methods — can be synthesized into a flexible framework for addressing classical problems from a modern field-theoretic viewpoint.

국문 초록 (Abstract)

본 논문은 현대 산란 진폭 기법을 바탕으로 고전 물리 문제에 적용 가능한 다양한
방법론을 탐색한다. 비록 양자장론에 기원을 두고 있지만, 전체적인 목표는 이러한
기법들을 고전역학적 현상에 대한 새로운 관점과 계산 도구로 활용하는 데에 있다.
먼저, 중력 이체계에서 중심질량계를 넘어서는 일반 좌표계에서의 푸앵카레
대칭을 구현함으로써, 산란 진폭 기반 해밀토니안이 만족해야 할 대칭 조건을 제
시한다. 이어서, 스칼라 장 이론에서 양자 오프쉘 재귀 관계(off-shell recursion
relation)를 이용한 단면적 계산을 통해, 향후 고전계 분석에 활용 가능한 체계적
인 섭동 방법론을 습득하고자 한다. 마지막으로, 자기 홀극 배경에서의 전하-홀극
산란 문제에 대해 부분파 전개와 KMOC 형식을 결합하여, 위상학적 구조를 갖는
계에서 고전 물리량을 효과적으로 추출할 수 있음을 보인다.
이러한 연구들은 대칭 원리, 재귀적 계산, 반고전적 기법 등을 통합한 산란
진폭 방법론이 고전 물리 문제를 현대 장론적 관점에서 효과적으로 다룰 수 있는
유연한 도구임을 보여준다.
이 학위논문은 [1–4]의 논문을 바탕으로 한다.

목차 (Table of Contents)

• Abstract 1
• Contents 2
• 1. Introduction 5
• 2. Poincaré Symmetry of Binary Dynamics in the Post-Minkowskian Approach 8
• 2.1 Introduction to Effective Field Theory and Scattering Amplitudes for Classical Gravitational Dynamics 8
• 2.1.1 Traditional Perturbative Approaches to Binary Dynamics 9
• 2.1.2 Effective Field Theory for Binary Dynamics 11
• 2.1.3 Scattering Amplitudes and Post-Minkowskian formalism 12
• 2.2 Preliminaries 16
• 2.2.1 Two boy effective Hamiltonian from scattering amplitudes 16
• 2.2.2 COM post-Minkowskian Hamiltonian 17
• 2.2.3 1PM effecitve Hamiltonian for spinning compact bodies 19
• 2.2.4 Poincar´e algebra 22
• 2.3 Poincar´e generators for non-spinning binary system 24
• 2.3.1 Non-spinning 1PM Poincar´e generators 24
• 2.3.2 Non-spinning 2PM Poincar´e generators 27
• 2.4 1PM Poincar´e generators for spinning compact bodies 33
• 2.4.1 Thomas-Wigner rotation in a lab frame 33
• 2.4.2 Vertex parameter 34
• 2.4.3 Boost generator 35
• 2.5 Summary and Outlook 42
• 3 Off-Shell Recursions for Cross Sections 44
• 3.1 Introduction and Preliminaries 44
• 3.1.1 Berends-Giele recursion and Classical Pertubiner 45
• 3.1.2 Quantum Perturbinber and Quantum off-shell recursion 47
• 3.1.3 S-matrix unitarity and Largest Time Equation 51
• 3.2 Action formalism for Largest Time Equation 57
• 3.2.1 The doubling prescription 57
• 3.2.2 Dyson-Schwinger equation in doubling prescription 60
• 3.3 Off-Shell Recursions for Differential Cross-Sections 61
• 3.3.1 Quantum Perturbiner for doubling prescription 62
• 3.3.2 Constructing recursion relations and obtaining amplitudes 66
• 3.3.3 From Off-Shell Currents to 2 → n cross sections 71
• 3.4 Differential cross-section from the recursions 77
• 3.4.1 Filtered off-shell currents up to three-loop level 77
• 3.4.2 Comparing with the differential cross-section 78
• 3.5 Summary and Outlook 80
• 4 Classical observables from partial wave amplitudes 83
• 4.1 Introduction to Magnetic Monopoles and KMOC formalism 83
• 4.1.1 Electromagnetic Duality and Magnetic Monopoles 83
• 4.1.2 Monopoles in Gauge Theory 85
• 4.1.3 Scattering Amplitudes and Magnetic Monopoles 86
• 4.1.4 KMOC formalism 89
• 4.2 Preliminaries 92
• 4.2.1 Classical Perturbation for charge-monopole scattering 92
• 4.2.2 Helicity basis for Partial wave expansion 93
• 4.2.3 Partial wave in the helicity basis 98
• 4.3 Classical impulse from partial wave 103
• 4.3.1 Radial action 103
• 4.3.2 Coulomb scattering 104
• 4.3.3 KMOC via Clebsch-Gordan 107
• 4.3.4 KMOC via saddle point 110
• 4.4 Charge-monopole scattering 113
• 4.4.1 Classical impulse 114
• 4.4.2 Wave equation and S-matrix116
• 4.4.3 Clebsch-Gordan approach 118
• 4.4.4 Saddle point approach124
• 4.5 Summary and Outlook 128
• 5 Conclusion 130
• A Appendix to Chapter 4 132
• A.1 Wigner and Bessel functions 132
• A.2 Completeness Relation in the Spinor Basis 136
• Bibliography 137
• 초록 152
• 감사의 글 153