多體物理
Many Body Physics
| 節 | 週一 |
|---|---|
5 13:20–14:10 | 多體物理 SC159（光復） 3 節連堂 |
6 14:20–15:10 | |
7 15:30–16:20 |
* 根據陽明交大上課時間表所列
The physical world, from the behavior of electrons in solids to the structure of atomic nuclei and the properties of quantum fluids, is fundamentally governed by the interactions between a vast number of constituent particles. While single-particle descriptions provide a crucial starting point, they typically fall short in capturing the rich physics of collective phenomena and emergent properties that arise solely from these interactions. Phenomena such as superconductivity, magnetism, the fractional quantum Hall effect, and the properties of strongly correlated materials cannot be understood without a theoretical framework capable of addressing the complex interplay of many interacting degrees of freedom. The course "Many-Body Physics" provides a formal introduction to the theoretical tools and conceptual frameworks necessary for describing interacting systems that underlie much of modern condensed matter physics, quantum chemistry, nuclear physics, and even aspects of high-energy physics. Methodologically, the course is built around the path integral approach to many-body physics. Rather than developing operator-based perturbation theory as the primary tool, we will formulate the many-body problem in terms of functional integrals over coherent states of bosonic and fermionic (Grassmann) fields. This perspective offers a unified language in which the quantum mechanics of interacting systems and their statistical mechanics at finite temperature appear on equal footing, connected simply by a Wick rotation to imaginary time. The path integral formalism provides a natural and systematic route to perturbation theory and Feynman diagrams, to the treatment of symmetries and their spontaneous breaking, to mean-field and saddle-point approximations via the identification of stationary field configurations, and to the study of collective fluctuations through the expansion of the action beyond the saddle point. It also furnishes the most direct bridge to renormalization group ideas and to the effective field theory description of low-energy, long-wavelength physics — techniques that will recur throughout the course and that are indispensable in the contemporary research literature. This course serves as a crucial bridge between foundational quantum mechanics and statistical mechanics and the advanced topics encountered in contemporary research literature and specialized fields.
Quantum mechanics & statistical physics
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This course provides a graduate-level introduction to quantum many-body physics with a strong emphasis on path-integral and functional-integral methods. Rather than treating functional integrals as an auxiliary reformulation of operator many-body theory, the course develops them as a central calculational and conceptual framework. Homework and Class Participation: 100% Students will be evaluated based entirely on homework assignments and class participation. Grading Method: This course will be graded on a Successful/Unsuccessful basis. Students who satisfactorily complete the course requirements will receive a grade of Successful; those who do not meet the requirements will receive a grade of Unsuccessful.
| 週次 | 主題 |
|---|---|
| 第 1 週 | From Many-Particle Quantum Mechanics to Quantum Fields 2026-09-07(一) |
| 第 2 週 | Coherent States and Bosonic Path Integrals 2026-09-14(一) |
| 第 3 週 | Grassmann Variables and Fermionic Functional Integrals 2026-09-21(一) |
| 第 4 週 | Finite-Temperature Field Theory and Generating Functionals 2026-09-28(一) |
| 第 5 週 | Interactions, Wick's Theorem, and Feynman Diagrams 2026-10-05(一) |
| 第 6 週 | Response Functions, Polarization, and RPA 2026-10-12(一) |
| 第 7 週 | Hubbard--Stratonovich Transformations and Emergent Fields 2026-10-19(一) |
| 第 8 週 | Saddle Points, Mean-Field Theory, and Gaussian Fluctuations 2026-10-26(一) |
| 第 9 週 | Superconductivity as a Functional-Integral Theory 2026-11-02(一) |
| 第 10 週 | Magnetism, Order Parameters, and Quantum Critical Actions 2026-11-09(一) |
| 第 11 週 | Renormalization Group from the Functional Integral 2026-11-16(一) |
| 第 12 週 | Quantum Impurity Models and Constrained Functional Integrals 2026-11-23(一) |
| 第 13 週 | Real-Time and Nonequilibrium Functional Integrals 2026-11-30(一) |
| 第 14 週 | Effective Field Theory, Emergence, and Synthesis 2026-12-07(一) |
| 第 15 週 | Spin coherent-state path integrals 2026-12-14(一) |
| 第 16 週 | Berry phases in quantum magnets 2026-12-21(一) |
Negele & Orland: Quantum Many-particle Systems Fetter & Walecka: Quantum Theory of Many-Particle Systems Altland & Simons: Condensed Matter Field Theory
- 地點
- 教師未提供此項資料
- 時間
- By appointment
- 聯絡方式
- kirchner@nycu.edu.tw