大额外维模型中引力子与光子的散射截面

论文摘要

基于高频引力波电磁响应的实验探测和统一场论中额外维模型的唯象研究,采用大额外维模型（LED）分析了Kaluza-Klein（KK）引力子与光子的相关散射过程,计算了反映散射几率的非极化微分截面,并在同等微扰阶数下,分别在线性量子引力理论（LQG）和广义相对论（GR）中研究了同一物理过程,对三者的理论结果做了比较分析,得出了有物理意义的结论。结果显示,它们都在趋前方向即小角度散射角范围内出现峰值,并且LED中相关过程的计算数值远大于LQG中的相应值,这是由于（大）额外维模型中引力子的大量KK态求和的结果;此外,在大额外维模型中相应过程的非极化散射截面会随着额外维度参数的增加而减小。此研究对于双光子的散射、引力的康普顿散射以及电磁场背景中引力子与光子的转化（用于探测高频引力波）具有实验指导意义,进而对于（大）额外维模型的唯象研究以及量子引力的理论探索也将提供学术参考。

论文目录

• 摘要
• ABSTRACT
• 1 Introduction and Motivation
• 1.1 Research Background
• 1.2 Study Motivation
• 2 Classical and Quantum Scattering Theory
• 2.1 Classical Scattering Theory
• 2.2 Quantum Scattering Theory
• 2.2.1 Partial Wave Method and Born Approximation Method
• 2.2.2 Formal Scattering Theory and C.M.S &Lab. Coordinate Systems
• 2.3 Several Relevant Processes in Scattering Viewpoint
• 2.3.1 Perturbative Photon Flux Caused by GWs Propagating in External Magnetic Field and Background EMW
• 2.3.2 Gravitational Light Bending in Semi-Quantum Approach
• 2.3.3 Gravitational Scattering of Light by Light in Gravitational Potential Scenario
• 2.4 Summary
• 3 General Relativity and Linearized Quantum Gravity
• 3.1 Special and General Relativity
• 3.2 Linearization and Gravitational Waves
• 3.3 Quantization and Linearized Quantum Gravity
• 3.3.1 The Lagrangian and Feynman rules
• 3.3.2 Graviton-Compton scattering
• 3.3.3 Graviton Mediated Scalar-Photon Scattering
• 3.3.4 Graviton mediated photon-photon scattering
• 3.4 Summary
• 4 Standard Model and Large Extra Dimensional Model
• 4.1 Electrodynamics and Quantum Electrodynamics （QED）
• 4.2 Electroweak Unification Theory and Quantum Chromodynamics （QCD）
• 4.3 Beyond the Standard Model and Extra Dimensional Models （ED）
• 4.3.1 Unification and the Hierarchy Problem
• 4.3.2 Kaluza-Klein Theory
• 4.3.3 Extra Dimensions and Compactification
• 4.3.4 KK-Excitations and KK-Gravitons
• 4.3.5 The Lagrangian and Relevant Feynman Rules
• 4.3.7 KK-Graviton Compton Scattering
• 4.3.8 KK-Graviton Mediated Scalar-Photon Scattering
• 4.3.9 KK-Graviton Mediated Photon-Photon Scattering
• 4.3.10 Summary
• 5 Conclusions and Outlook
• Acknowledgements
• References
• Appendix