Group Theory in a Nutshell for Physicists

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This modern textbook on group theory is tailored for physicists, addressing a crucial mathematical subject that underpins various fields of theoretical physics, including atomic, condensed matter, particle physics, and string theory. It is particularly vital for understanding fundamental forces. The book fills a gap by offering a user-friendly and classroom-tested resource that emphasizes the aspects of group theory most relevant to physicists. A. Zee guides readers from the basic concept of a group to advanced topics, such as theories based on gauge groups that could unify three of the four fundamental forces. Additionally, it includes a concise review of the necessary linear algebra, making it suitable for self-study. The text covers applications across multiple areas of physics, including field theory, particle physics, and relativity. Key topics addressed are finite groups and character tables, various representations, the Weyl, Dirac, and Majorana equations, and the relationship between group theory and the expanding universe, among others. This essential resource serves as a textbook for students and a valuable reference for researchers. It features a brief, self-contained treatment of linear algebra, and an online illustration package is available for professors, along with a solutions manual exclusive to educators.