2023年量子场论课程主页

课程信息

上课时间：每周一上午10:10-12:00，每周三下午3:10-5:00

上课地点：三教501

答疑时间: 每周三, 7pm - 8:30pm

答疑地点：物理学院南楼433

助教：党金龙

助教邮箱：dangjl@stu.pku.edu.cn

课程讲义

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作业

（1）第一、二周作业 答案
（2）第三、四周作业（截止日期10月16日） 答案
（3）第五、六周作业（截止日期11月1日） 答案
（4）第四次作业（截止日期11月20日） 答案
（5）第五次作业（截止日期11月27日） 答案
（6）第六次作业（截止日期12月11日） 答案
（7）第七次作业（截止日期12月27日） 答案

课程讨论班

时间：周四，7pm-9pm

地点：物理南楼408

11月16日，陈丰业：施温格效应

11月30日，阮洪奕：Casimir效应

12月7日，孙韫博：霍金辐射

课程讨论班为自愿参加的活动。感兴趣的同学请选择下面列出的某个主题，或自主提出的一个主题，在9月28日前发邮件向任课老师报名主讲。主讲老师将根据报名情况协调安排报告顺序和时间，由报告同学在指定的日期作黑板报告，并鼓励就所讨论的主题撰写阅读笔记。（感谢陈豪和李依蓓同学对参考文献的贡献！）

• Topological objects in QFT:
  1. M. Shifman, Advanced Topics in Quantum Field Theory, Chapter 2 and 3
  2. A. Zee, Quantum Field Theory in a Nutshell, Part V
  3. David Tong, TASI Lectures on Solitons:Instantons, Monopoles, Vortices and Kinks [hep-th/0509216]

• 范德瓦尔斯力与量子场论:
  1. Claude Itzykson and Jean-Bernard Zuber, Quantum Field Theory, Section 7-3-3 Van der Waals Forces at Large Distances
  2. Barry R. Holstein, The van der Waals interaction
  3. I.E. Dzyaloshinskii et al, The general theory of van der Waals forces

• 朗道方程与Cutkosky法则:
  1. Matthew D. Schwartz, Quantum Field Theory and the Standard Model, Section 24.1 The optical theorem, in particular Section 24.1.2 Cutting rules
  2. L. D. Landau, On analytic properties of vertex parts in quantum field theory
  3. R. E. Cutkosky, Singularities and discontinuities of Feynman amplitudes
  4. Claude Itzykson and Jean-Bernard Zuber, Quantum Field Theory, Section 6-3 Analyticity properties
  5. Paokuan Chin and E. T. Tomboulis, Nonlocal vertices and analyticity: Landau equations and general Cutkosky rule, can also be found on [arXiv:1803.08899]

• 施温格效应:
  1. Julian Schwinger, On Gauge Invariance and Vacuum Polarization, can also be found on https://journals.aps.org/pr/abstract/10.1103/PhysRev.82.664
  2. Claude Itzykson and Jean-Bernard Zuber, Quantum field theory, Sections 4-3-3 & 4-3-4
  3. Gerald V. Dunne, The Heisenberg-Euler Effective Action: 75 years on, [arXiv:1202.1557]; Heisenberg-Euler Effective Lagrangians: Basics and Extensions, [arXiv:hep-th/0406216], Section 1 Introduction

• Unruh效应:
  1. W. G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870. (https://journals.aps.org/prd/abstract/10.1103/PhysRevD.14.870)
  2. W. G. Unruh and R. M. Wald, What happens when an accelerating observer detects a Rindler particle, Phys. Rev. D 29 (1984) 1047–1056. (https://journals.aps.org/prd/abstract/10.1103/PhysRevD.29.1047)
  3. The Unruh effect and its applications (https://arxiv.org/pdf/0710.5373.pdf)
  4. S. Carroll, Spacetime and Geometry, Chapter 9
  5. T. Hartman's Lecture Notes, Section 3 (http://www.hartmanhep.net/topics2015/gravity-lectures.pdf)

• 霍金辐射:
  1. Hawking, S.W. Particle creation by black holes. Commun.Math. Phys. 43, 199–220 (1975).
  2. S. Carroll, Spacetime and Geometry, Chapter 9
  3. T. Hartman's Lecture Notes, Section 3 (http://www.hartmanhep.net/topics2015/gravity-lectures.pdf)

• S矩阵元理论:Froissart界,因果性、解析性与幺正性:
  1. Eden, Landshoff, Olive and Polkinghorne, The Analytic S-Matrix
  2. Itykson and Zuber, Quantum Field Theory, Section 5-3
  3. V.N. Gribov, The Theory of Complex Angular Momenta, Section 1

• 量子反常:
  1. Quantum field theory anomalies in condensed matter physics (https://scipost.org/SciPostPhysLectNotes.62/pdf)
  2. Jeffrey Harvey, TASI 2003 LECTURES ON ANOMALIES [hep-th/0509097]
  3. David Tong, Lectures on Gauge Theory (http://www.damtp.cam.ac.uk/user/tong/gaugetheory.html)
  4. Yuji Tachikawa, Lecture on anomalies and topological phases (https://member.ipmu.jp/yuji.tachikawa/lectures/2019-top-anom/)

• 温伯格软定理:
  1. S. Weinberg, Infrared Photons and Gravitons https://journals.aps.org/pr/abstract/10.1103/PhysRev.140.B516
  2. S. Weinberg, The quantum theory of fields, Volume 1, Section 13.1 Soft Photon Amplitudes
  3. Matthew D. Schwartz, Quantum Field Theory and the Standard Model, Section 36.3 Soft interactions
  4. Andrew Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory [arXiv:1703.05448]

• 超导与有效场论:
  1. A. Zee, Quantum Field Theory in a Nutshell, Section V.4
  2. Matthew D. Schwartz, Quantum Field Theory and the Standard Model, Section 28.3.2 Superconductors
  3. Joseph Polchinski, Effective Field Theory and the Fermi Surface [arXiv:hep-th/9210046v2]

• 量子场论中的纠缠熵:
  1. E. Witten, Notes on Some Entanglement Properties of Quantum Field Theory [1803.04993]
  2. Horacio Casini and Marina Huerta, (TASI 2021) Lectures on entanglement in quantum field theory [2201.13310]
  3. Matthew Headrick, Lectures on entanglement entropy in field theory and holography [1907.08126]

• 超流理论:
  1. M. Kardar, Statistical Physics of Fields, Sections 2.1 -- 3.3
  2. A. Zee, Quantum Field Theory in a Nutshell, Section V.1 Superfluids
  3. A. Schmitt, Introduction to superfluidity: Field-theoretical approach and applications [arXiv:1404.1284]

• 分数统计与陈西蒙斯理论:
  1. David Tong, The Quantum Hall Effect, Chapter 3 and 5 (http://www.damtp.cam.ac.uk/user/tong/qhe.html)
  2. A. Zee, Quantum Field Theory in a Nutshell, Part VI
  3. E. Witten, Three Lectures On Topological Phases Of Matter [1510.07698]

• CPT定理与自旋统计定理:
  1. Raymond F. Streater and Arthur S. Wightman, "PCT, Spin and Statistics, and All That", Chapter 4
  2. Weinberg, The Quantum Theory of Fields, Vol 1, Section 5.7 and 5.8
  3. Schwartz, Quantum Field Theory and the Standard Model, Chapter 12

• 量子场论与渐近级数:
  1. Eric Sharpe, Course Reading: Special functions independent study: Asymptotic series
  2. F. J. Dyson, Divergence of Perturbation Theory in Quantum Electrodynamics https://journals.aps.org/pr/abstract/10.1103/PhysRev.85.631
  3. D. I. Kazakov and D. V. Shirkov, Asymptotic Series of Quantum Field Theory and Their Summation

• Weinberg-Witten no-go theorem:
  1. Weinberg and Witten, Limits on massless particles, Physics Letters B. 96 (1–2): 59–62 (https://lib-extopc.kek.jp/preprints/PDF/1981/8101/8101322.pdf)
  2. Florian Loebbert, The Weinberg-Witten theorem on massless particles: an essay (https://core.ac.uk/download/pdf/210849216.pdf)

• 超对称与指标定理:
  1. Luis Alvarez-Gaume, Supersymmetry and the Atiyah-Singer Index Theorem (http://www.damtp.cam.ac.uk/user/tong/susy/index.pdf)
  2. H. Oogori, Lecture 8: Supersymmetry and index theorems
  3. A master thesis, (https://www.diva-portal.org/smash/get/diva2:768786/FULLTEXT01.pdf)

• 量子混沌与SYK模型:
  1. A. Kitaev, “A simple model of quantum holography,” KITP strings seminar and Entanglement 2015 program (http://online.kitp.ucsb.edu/online/entangled15/)
  2. S. Sachdev and J. Ye, “Gapless spin-fluid ground state in a random quantum Heisenberg magnet,”Phys. Rev. Lett. 70 (May, 1993) 3339–3342.
  3. Vladimir Rosenhaus, An introduction to the SYK model [1807.03334]
  4. Joseph Polchinski and Vladimir Rosenhaus, The Spectrum in the Sachdev-Ye-Kitaev Model [1601.06768]

• 卡西米尔效应:
  1. Schwartz, Quantum Field Theory and the Standard Model, Section 15
  2. G. Plunien, Berndt Muller, W. Greiner, The Casimir Effect (https://doi.org/10.1016/0370-1573(86)90020-7)
  3. Advances in the Casimir Effect, Part 1 (https://academic.oup.com/book/359)

• 自旋3/2场理论:
  1. W. Rarita, J. Schwinger, On a theory of particles with half integral spin https://journals.aps.org/pr/abstract/10.1103/PhysRev.60.61
  2. W. Qiu, F. Sun, H. Zhang, On the Quantum Theory of Massless Spin-3/2 Field in Minkowski Spacetime [arXiv:hep-th/0601011v5]
  3. S. Deser, V. Pascalutsa and A. Waldron, Massive Spin 3/2 Electrodynamics [arXiv:hep-th/0003011v2]
  4. G. Velo and D. Zwanziger, Propagation and Quantization of Rarita-Schwinger Waves in an External Electromagnetic Potential
  5. G. Velo and D. Zwanziger, Noncausality and Other Defects of Interaction Lagrangians for Particles with Spin One and Higher
  6. T.-P. Hack, M. Makedonski, A No-Go Theorem for the Consistent Quantization of Spin 3/2 Fields on General Curved Spacetimes [arXiv:1106.6327v3]

• 马约拉纳费米子:
  1. M. D. Schwartz, Quantum Field Theory and the Standard Model, Section 10.6 Majorana and Weyl fermions & 11.3 Majorana spinors
  2. M. Srednicki, Quantum Field Theory, Sections 36, 37, 39, 40, 41, 42, 49
  3. Aran Sivaguru, Majorana Fermions (QFFF MSc Dissertation)

• 庞加莱群的表示:
  1. E. Wigner, On Unitary Representations of the Inhomogeneous Lorentz Group
  2. S. Weinberg, The quantum theory of fields, Volume 1, Section 2.4
  3. Joseph Maciejko, Representations of Lorentz and Poincaré groups
  4. Peter Woit, The Poincaré Group and its Representations, Section 42