Group Theory for Physicists: With Applications

Group theory helps readers in understanding the energy spectrum and the degeneracy of systems possessing discrete symmetry and continuous symmetry. The fundamental concepts of group theory and its applications are presented with the help of solved problems and exercises. The text covers two essential aspects of group theory, namely discrete groups and Lie groups. Important concepts including permutation groups, point groups and irreducible representation related to discrete groups are discussed with the aid of solved problems. Topics such as the matrix exponential, the circle group, tensor products, angular momentum algebra and the Lorentz group are explained to help readers in understanding the quark model and theory composites. Real-life applications including molecular vibration, level splitting perturbation, crystal field splitting and the orthogonal group are also covered. Application-oriented solved problems and exercises are interspersed throughout the text to reinforce understanding of the key concepts.

群論幫助讀者理解具有離散對稱性和連續對稱性的系統的能譜和退化。本書通過解決問題和練習來介紹群論的基本概念及其應用。該書涵蓋了群論的兩個重要方面，即離散群和李群。通過解決問題的方式討論了與離散群相關的重要概念，包括置換群、點群和不可約表示。解釋了矩陣指數、圓圈群、張量乘積、角動量代數和洛倫茲群等主題，以幫助讀者理解夸克模型和理論組合。還介紹了分子振動、能級分裂微擾、晶體場分裂和正交群等現實應用。書中穿插了應用導向的解決問題和練習，以加強對關鍵概念的理解。