Continuous Groups for Physicists

The book is designed for graduate students and researchers working in the field of theoretical physics and related fields.

Narasimhaiengar Mukunda (Author), Subhash Chaturvedi (Author)

9781009187053, Cambridge University Press

Hardback, published 5 January 2023

300 pages
24.7 x 18.9 x 1.8 cm, 0.63 kg

'… this book is a very useful and very well conceived introductory course to the theory of Lie groups, Lie algebras and their representation theory, mainly intended for theoretical physicists. The style makes the book very readable, with special focus on the physical interpretation, with problems and references that lead the reader to more specialized topics.' Rutwig Campoamor Stursberg, ZB Math

Continuous Groups for Physicists is written for graduate students as well as researchers working in the field of theoretical physics. The text has been designed uniquely and it balances coverage of advanced and non-standard topics with an equal focus on the basic concepts for a thorough understanding. The book describes the general theory of Lie groups and Lie algebras, the passage between them, and their unitary/ Hermitian representations in the quantum mechanical setting. The four infinite classical families of compact simple Lie groups and their representations are covered in detail. Readers will benefit from the discussions on topics like spinor representations of real orthogonal groups, the Schwinger representation of a group, induced representations, systems of coherent states, real symplectic groups important in quantum mechanics, Wigner's theorem on symmetry operations in quantum mechanics, ray representations of Lie groups, and groups associated with non-relativistic and relativistic space-time.

1. Basic Group Theory and Representation Theory
2. The Symmetric Group
3. Rotations in 2 and 3 Dimensions, SU(2)
4. General Theory of Lie Groups and Lie Algebras
5. Compact Simple Lie Algebras – Classification and Irreducible Representations
6. Spinor Representations of the Orthogonal Groups
7. Properties of Some Reducible Group Representations, and Systems of Generalised Coherent States
8. Structure and some Properties and Applications of the Groups Sp(2n, R)
9. Wigner's Theorem, Ray Representations and Neutral Elements
10. Groups Related to Space-Time.

Subject Areas: Physics [PH]