Introduction to Many-Body Theory: From Action Principles to Path Integrals and Functional Methods
暫譯: 多體理論導論：從作用量原理到路徑積分與泛函方法
Vogl, Michael Rudolf
- 出版商: Springer
- 出版日期: 2026-10-08
- 售價: $3,430
- 貴賓價: 9.5 折 $3,258
- 語言: 英文
- 頁數: 340
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3032197651
- ISBN-13: 9783032197658
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相關分類:
物理學 Physics
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商品描述
This textbook provides a self-contained introduction to many-body theory that bridges the gap between the standard graduate curriculum and more research-oriented courses in many-body theory. The author systematically constructs the basic formalism of many-body theory, starting from Newton's second law, and subsequently develops action principles and symmetry-based techniques. Upon switching to quantum theory, second quantization and the Feynman path integral are introduced. After a treatment of statistical mechanics from an information-entropy perspective, which allows for a simple understanding of temperature dependent variational principles, the book switches to a coherent state path-integral formulation. This approach makes diagrammatic perturbation theory, linear response techniques, and renormalization group methods, which are treated in later parts of the book, accessible to a broad audience.
The content of the book is based on a set of lectures on the Quantum Theory of Solids that the author has taught at King Fahd University of Petroleum and Minerals (KFUPM) every year since 2022. With detailed, explicit computations and exercises at various difficulty levels, the book serves as a valuable resource for talented undergraduate students, graduate students, beginning researchers and instructors. While familiarity with variational calculus and functional integration is advantageous, the book systematically constructs the necessary tools as needed, making it self-contained, and mastery of the skills is not considered a prerequisite.
Each chapter of the book also includes a summary and a set of problems, separated into introductory and advanced levels. This setup allows readers to master concepts efficiently and helps develop their skills up to an advanced level.
商品描述(中文翻譯)
本教科書提供多體理論（many-body theory）的自成一體導論，銜接標準研究所課程與更偏向研究導向的多體理論課程之間的落差。作者從 Newton 第二運動定律出發，有系統地建構多體理論的基本形式體系，接著發展作用量原理（action principles）與以對稱性為基礎的技術。轉入量子理論後，書中介紹二次量子化（second quantization）與 Feynman 路徑積分（Feynman path integral）。在以資訊熵（information entropy）的觀點處理統計力學之後，讀者便能簡單理解與溫度相關的變分原理（temperature-dependent variational principles）；接著本書轉而採用相干態路徑積分（coherent-state path-integral）形式。這種方法使後續章節所討論的圖示微擾理論（diagrammatic perturbation theory）、線性響應技術（linear response techniques）與重整化群方法（renormalization group methods），都能為廣泛的讀者所理解。
本書內容源自作者自 2022 年起，每年在 King Fahd University of Petroleum and Minerals（KFUPM）講授的「固體量子理論」（Quantum Theory of Solids）課程。書中提供詳細且明確的計算，以及不同難度層級的練習，因此是優秀大學生、研究生、初入門研究人員與教師的寶貴資源。雖然熟悉變分微積分（variational calculus）與泛函積分（functional integration）將有所助益，但本書會在需要時有系統地建構必要的工具，因此內容自成一體；讀者不必事先精通這些技能。
本書每一章皆包含摘要與一組問題，並區分為入門與進階兩個層級。這樣的編排能讓讀者有效掌握各項概念，並逐步培養達到進階程度的能力。
作者簡介
Michael Rudolf Vogl began his academic journey with a Bachelor's degree in Physics at Friedrich-Alexander-Universität Erlangen-Nürnberg, completing the program in August 2011 under the supervision of Michael Thies. He continued with a Master's degree under the guidance of Oleg Pankratov and Sam Shallcross, earning the degree in 2014 and receiving a thesis prize. He then pursued doctoral studies at the University of Texas at Austin, where he completed his PhD in May 2020 under the supervision of Gregory Fiete.
Immediately after completing his PhD, he was offered an Assistant Professor position at King Fahd University of Petroleum and Minerals. Due to COVID-related travel restrictions, he joined the university in September 2021, one year later than originally planned. Since then, he has been teaching quantum many-body theory to graduate students at King Fahd University of Petroleum and Minerals.
作者簡介(中文翻譯)
Michael Rudolf Vogl 在 Friedrich-Alexander-Universität Erlangen-Nürnberg 開始了他的學術生涯，主修物理學並取得學士學位；在 Michael Thies 指導下，他於 2011 年 8 月完成學業。之後，他在 Oleg Pankratov 與 Sam Shallcross 的指導下攻讀碩士學位，於 2014 年取得學位，並獲得論文獎。接著，他前往 University of Texas at Austin 攻讀博士，並在 Gregory Fiete 的指導下於 2020 年 5 月取得博士學位。
博士畢業後，他隨即獲聘為 King Fahd University of Petroleum and Minerals 的助理教授。由於 COVID-19 相關的旅行限制，他於 2021 年 9 月加入該校，比原訂計畫晚了一年。自此，他一直在 King Fahd University of Petroleum and Minerals 為研究生教授量子多體理論。
