Symmetry, Broken Symmetry, and Topology in Modern Physics: A First Course (Hardcover)

Written for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincaré invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.

這本書是為教學和自學而寫的，提供了對於群、代數、幾何和拓撲的全面且教學導向的介紹。它整合了這些概念的現代應用，僅需具備物理學高年級本科的基礎知識。它提供了對於群論、李代數和拓撲概念的平衡觀點，同時強調了許多現代應用，如洛倫茲和庞加莱不變性、相干態、量子相變、量子霍爾效應、拓撲物質和陳數等。從一開始就採用了基於例子的方法，並且書中包含了解題示例和信息框，以說明和擴展關鍵概念。書中包含了344個作業問題，教師可以獲得完整解答，學生則可以獲得其中172個問題的完整解答。