Symmetries in Physics: Group Theory Applied to Physical Problems (Springer Series in Solid-State Sciences)

Everyone knows that symmetry is fundamentally important in physics. On one hand, the symmetry of a system is often the starting point for general physical considerations, and on the other hand, particular problems may be solved in simpler and more elegant ways if symmetry is taken into account. This book presents the underlying theories of symmetry and gives examples of their application in branches of physics ranging from solid-state to high-energy physics via atomic and molecular physics. The text is as self-contained as possible, with as much mathematical formalism given as required. The main emphasis is on the theory of group representations and on the method of projection operators, this is a very powerful tool which is often treated only very briefly. Discrete symmetries, continuous symmetries and symmetry breaking are also discussed, and exercises are provided to stimulate the reader to carry out original work. Front Matter....Pages I-XI Introduction....Pages 1-3 Elements of the Theory of Finite Groups....Pages 4-17 Discrete Symmetry Groups....Pages 18-46 Representations of Finite Groups....Pages 47-86 Irreducible Representations of Special Groups....Pages 87-125 Tensor Operators and Expectation Values....Pages 126-138 Molecular Spectra....Pages 139-182 Selection Rules and Matrix Elements....Pages 183-202 Representations of Space Groups....Pages 203-229 Excitation Spectra and Selection Rules in Crystals....Pages 230-265 Lie Groups and Lie Algebras....Pages 266-310 Representations by Young Diagrams. The Method of Irreducible Tensors....Pages 311-317 Applications of the Theory of Continuous Groups....Pages 318-349 Internal Symmetries and Gauge Theories....Pages 350-405 Back Matter....Pages 406-463 Introduction Elements of the Theory of Finite Groups Discrete Symmetry Groups Representations of Finite Groups Irreducible Representations of Special Groups Tensor Operators and Expectation Values Molecular Spectra Selection Rules and Matrix Elements Representations of Space Groups Excitation Spectra and Selection Rules in Crystals Lie Groups and Lie Algebras Representations by Young Diagrams. The Method of Irreducible Tensors Applications of the Theory of Continuous Groups Internal Symmetries and Gauge Theories Appendices References Additional References Subject Index.