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"The theory of groups and group representations is an important part of mathematics with applications in other areas of mathematics as well as in physics. It is basic to the study of symmetries of physical systems. Its mathematical concepts are equally significant in understanding complex physical systems. It offers the necessary tools to describe, for instance, crystal structures, elementary particles with spin, both Galilean symmetric and special relativistic quantum mechanics, the fundamental properties of canonical commutation relations, and spinor representations of orthogonal groups extensively used in quantum field theory. Continuous Groups for Physicists introduces the ideas of continuous groups and their applications to graduate students and researchers in theoretical physics. The book begins with an introduction to groups and group representations in the context of finite groups. This is followed by a chapter on the special algebraic features of the symmetric groups. The authors then present the theory of Lie groups, Lie algebras, and in particular the classical families of compact simple Lie groups and their representations. Several interesting topics not often found in standard physics texts are then presented: the spinor representations of the real orthogonal groups, the real symplectic groups in even dimensions, induced representations, the Schwinger representation concept, the Wigner theorem on symmetry operations in quantum mechanics, and the Euclidean, Galilei, Lorentz, and Poincare groups associated with spacetime. The general methods and notions of quantum mechanics are used as background throughout"--
List of contents
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.
Summary
The book intends to focus on Lie group representations in the quantum context for graduate students and researchers taking courses in theoretical physics. Special emphasis is given to the explanation of the topics like Lie group families, spinors, real symplectic groups coherent states, their representations and Lie groups acting on space-time.
