EAN: 9783030943592

UNIVERSITEXT GROUPS AND SYMMETRIES - YVETTE K...

Groups and Symmetries: From Finite Groups to Lie Groups presents an introduction to the theory
of group representations and its applications in quantum mechanics. Accessible to advanced
undergraduates in mathematics and physics as well as beginning graduate students  the text
deals with the theory of representations of finite groups  compact groups  linear Lie groups
and their Lie algebras  concisely and in one volume. Prerequisites include calculus and linear
algebra. This new edition contains an additional chapter that deals with Clifford algebras 
spin groups  and the theory of spinors  as well as new sections entitled Topics in history
comprising notes on the history of the material treated within each chapter. (Taken together 
they constitute an account of the development of the theory of groups from its inception in the
18th century to the mid-20th.) References for additional resources and further study are
provided in each chapter. All chapters end with exercises of varying degree of difficulty  some
of which introduce new definitions and results. The text concludes with a collection of
problems with complete solutions making it ideal for both course work and independent study.
Key Topics include: Brisk review of the basic definitions of group theory  with examples
Representation theory of finite groups: character theory Representations of compact groups
using the Haar measure Lie algebras and linear Lie groups Detailed study of SO(3) and SU(2) 
and their representations Spherical harmonics Representations of SU(3)  roots and weights  with
quark theory as a consequence of the mathematical properties of this symmetry group Spin groups
and spinors

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