Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.
Table of Contents
General Properties of Groups and Mappings
Properties of Irreducible Representations
Continuous Groups (SO(N))
The SU(N) Groups and Particle Physics
General Treatment of Simple Lie Groups
Representations of the Poincaré Groups
Appendix A: Dirac Notion in Quantum Mechanics
Appendix B: Eigenstates of Angular Momentum in Quantum Mechanics
Appendix C: Group-Invariant Measure for SO(3)
Appendix D: Calculation of Roots for SO(n) and Sp(2r)
Appendix E: Covariant Normalization and Relativistic Scattering
Appendix F: Lagrangian Mechanics
Glossary of Mathematical Symbols
"This work seems to cover virtually all the problems of physics for which group theory is helpful … strikes a good balance between mathematics and physical applications and should be valuable to researchers. It is well printed and produced and the paperback edition is a good value."
-Aslib Book List
"The author has admirably fulfilled his aims. The material is tightly packed and no phrase is wasted … I liked the succinct way in which the subject was developed in this new book. It provides a firm foundation for further reading, especially those parts which the author 'squashed down' in the interest of brevity, and is a welcome addition to my bookshelf."
"Most group theorists would be astonished by what happens to their pets when physicists gets their hands on them, as in Groups, Representations and Physics by H.F. Jones. I'm not suggesting we teach quantum field theory to every algebraist, but they could learn an awful lot from the group-theoretic treatment of the vibrational modes of the water molecule."