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所在平台: Udemy |
课程主页: https://www.udemy.com/course/qft-in-curved-spacetime-hawking-radiation-unruh-effect/
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**课程名称：** 弯曲时空中的量子场论：霍金辐射与乌恩鲁赫效应 **课程概述：** 本门高级课程深入探讨量子场论（QFT）与广义相对论的交叉领域，重点关注支配弯曲时空中量子场的理论和数学结构。课程面向研究生、研究人员以及理论物理领域的专业人士。 **核心内容（不分先后）：** * **弯曲时空中量子场论基础：** * 非闵可夫斯基几何中量子场的定义。 * 真空态、粒子产生及半经典方法。 * **霍金辐射：** * 黑洞辐射的推导与分析。 * 对黑洞热力学与熵的启示。 * 黑洞寿命与蒸发过程。 * 全息原理与圈量子引力学的见解。 * **乌恩鲁赫效应：** * 均匀加速观测者感知到的真空涨落。 * 与林德勒视界及热效应的理论联系。 * 林德勒与闵可夫斯基真空，以及Bogolyubov系数的作用。 * 加速、温度与熵之间的联系。 * **引力量子修正的数学框架：** * 路径积分形式及其在弯曲时空中的应用。 * 热核方法、Zeta函数正则化与重整化。 * 欧几里得量子引力与有效作用方法。 * 弯曲时空中的洛伦兹群与庞加莱群表示。 * **在量子引力与宇宙学中的应用：** * 有效场论对广义相对论的量子修正。 * 膨胀宇宙中的标量场与暴胀模型。 * 卡西米尔力、半经典引力与涌现时空模型。 **学习目标：** 完成本课程后，学员将对弯曲时空中量子场论的核心理论原则及其对基本物理学的意义有深入透彻的理解。课程将为参与者提供进行量子引力、黑洞物理学和宇宙学等前沿研究的工具。 **先修要求：** 学员应具备扎实的量子场论和广义相对论基础。强烈建议熟悉高级数学方法，包括泛函分析和微分几何。课程的起始部分会回顾课程中广泛使用的相关量子场论概念。 **课程形式：** 课程结构包含“形式”讲座（旨在激发物理和数学直觉）以及对经典和当代研究文献的批判性讨论。课程力求提供对该主题严谨而全面的理解。 **教学大纲：** 无
This advanced course examines the interface of quantum field theory (QFT) and general relativity, focusing on the theoretical and mathematical structures that govern quantum fields in curved spacetime. The course is intended for graduate students, researchers, as well as professionals in theoretical physics.The syllabus includes the following key topics (not necessarily in this order):Foundations of QFT in Curved SpacetimeDefinition of quantum fields in non-Minkowskian geometries.Vacuum states, particle creation, and the semiclassical approach.Hawking RadiationDerivation and analysis of black hole radiation.Implications for black hole thermodynamics and entropy.Black hole lifetime and evaporation processesInsights from the holographic principle and Loop Quantum GravityThe Unruh EffectExamination of vacuum fluctuations as perceived by uniformly accelerated observers.Theoretical connection to the Rindler horizon and thermal effects.Rindler and Minkowski vacua, and the role of Bogolyubov coefficientsConnection between acceleration, temperature, and entropyMathematical Framework for the Calculation of Quantum Corrections to GravityPath integral formulation and its application to curved spacetimeHeat kernel methods, zeta function regularization, and renormalizationEuclidean quantum gravity and effective action approachesLorentz and Poincaré group representations in curved spacetimeApplications to Quantum Gravity & CosmologyQuantum corrections to General Relativity from effective field theoryScalar fields in expanding universes and inflationary modelsCasimir force, semiclassical gravity, and emergent spacetime modelsBy the end of the course, students will develop a thorough understanding of the core theoretical principles of QFT in curved spacetime, as well as their implications for fundamental physics. The course will equip participants with the tools necessary to engage in more advanced research in quantum gravity, black hole physics, and cosmology.Prerequisites:Participants should have a solid foundation in QFT and general relativity. Familiarity with advanced mathematical methods, including functional analysis and differential geometry, is strongly recommended. However, the first section recalls those relevant concepts of QFT, which are used extensively throughout the course.Course Format:The course is structured around "formal" lectures (aiming to stimulate physical and mathematical intuition), and critical discussions of seminal and contemporary research literature. It aims to provide a rigorous and comprehensive understanding of the subject.
