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I'm looking for a text that covers group theory and its applications for QM and QFT, targeted towards an audience that knows their QM but is ignorant of everything quantum fieldy. Any recommendations?
dextercioby said:I've always liked the group theory book for physicists by Wu Ki Tung published by World Scientific in 1984.
Group theory is a branch of mathematics that deals with the study of groups, which are mathematical objects that have a set of elements and a binary operation that combines any two elements to form a third element. It is a fundamental concept in abstract algebra and has applications in various fields such as physics, chemistry, and computer science.
The basic concepts in group theory include group operations, identity element, inverse elements, commutativity, subgroup, coset, and normal subgroup. Group operations are binary operations that combine two elements to form a third element. The identity element is an element that, when combined with any other element, results in the same element. Inverse elements are elements that, when combined with another element, result in the identity element. Commutativity refers to the property of a group operation where the order of the elements does not affect the result. Subgroup, coset, and normal subgroup are subsets of a group that have specific properties.
Some recommended textbooks for learning group theory include "Abstract Algebra" by David S. Dummit and Richard M. Foote, "A Book of Abstract Algebra" by Charles C. Pinter, "Algebra: Chapter 0" by Paolo Aluffi, "Group Theory" by W.R. Scott, and "Basic Algebra" by Nathan Jacobson. These textbooks cover the basic concepts and applications of group theory and are suitable for both beginner and advanced readers.
Group theory has many real-world applications, including in physics, chemistry, and computer science. In physics, group theory is used to study the symmetries of physical systems and to describe the fundamental forces of nature. In chemistry, group theory is used to study the symmetries of molecules and crystals. In computer science, group theory is used in cryptography to ensure secure communication and data transfer.
The best way to approach studying group theory is to first familiarize yourself with the basic concepts and definitions. Then, practice solving problems and proofs to solidify your understanding. It is also helpful to read and understand different examples and applications of group theory. Collaborating with others and discussing concepts can also aid in understanding and retention. Additionally, regularly reviewing and practicing problems is key to mastering group theory.