Group theory for physicists : with applications /
Pichai Ramadevi, Varun Dubey.
Bok Engelsk 2019 · Electronic books.
| Annen tittel | |
|---|---|
| Medvirkende | Dubey, Varun, (author.)
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| Utgitt | Cambridge University Press
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| Omfang | 1 online resource (xiv, 159 pages) : : digital, PDF file(s).
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| Opplysninger | Title from publisher's bibliographic system (viewed on 11 Oct 2019).. - Cover -- Group Theory for Physicists -- Title -- Copyright -- Contents -- Figures -- Tables -- Preface -- 1 Introduction -- 1.1 Definition of a Group -- 1.2 Subgroups -- 1.3 Conjugacy Classes -- 1.4 Further Examples of Groups -- 1.5 Homomorphism of Groups -- 1.6 The Symmetric Group -- 1.7 Direct and Semidirect Products -- Exercises -- 2 Molecular Symmetry -- 2.1 Elements of Molecular Symmetry -- 2.2 The Symmetry Group of a Molecule -- 2.3 Symmetry Point Groups -- Exercises -- 3 Representations of Finite Groups -- 3.1 Vector Spaces -- 3.2 Group Action on Vector Spaces -- 3.3 Reducible and Irreducible Representations -- 3.4 Irreducible Representations of Point Groups -- 3.5 The Regular Representation -- 3.6 Tensor Product of Representations -- 3.7 Decomposition of Reducible Representations -- 3.8 Irreducible Representations of Direct Products -- 3.9 Induced Representations -- Exercises -- 4 Elementary Applications -- 4.1 General Considerations -- 4.2 Level Splitting under Perturbation -- 4.3 Selection Rules -- 4.4 Molecular Vibrations -- Exercises -- 5 Lie Groups and Lie Algebras -- 5.1 The Circle Group U(1) -- 5.2 The Matrix Exponential -- 5.3 Finite Dimensional Lie Algebras -- 5.4 Semisimple Lie Algebras -- 5.5 Lie Algebra of a Lie Group -- 5.6 Examples of Lie Groups -- 5.7 Compact Simple Lie Algebras -- Exercises -- 6 Further Applications -- 6.1 Continuous Symmetry and Constant of Motion -- 6.2 Tensor Product Rule for -- Irreducible Representations -- 6.3 Elementary Particles in Nuclear and Particle Physics -- 6.4 Quark Model -- 6.5 Noncompact Groups -- 6.6 Dynamical Symmetry in Hydrogen Atom -- Exercises -- Appendix A: Maschke's Theorem -- Appendix B: Schur's Lemma -- Bibliography -- Index.. - Group theory helps readers in understanding the energy spectrum and the degeneracy of systems possessing discrete symmetry and continuous symmetry. The fundamental concepts of group theory and its applications are presented with the help of solved problems and exercises. The text covers two essential aspects of group theory, namely discrete groups and Lie groups. Important concepts including permutation groups, point groups and irreducible representation related to discrete groups are discussed with the aid of solved problems. Topics such as the matrix exponential, the circle group, tensor products, angular momentum algebra and the Lorentz group are explained to help readers in understanding the quark model and theory composites. Real-life applications including molecular vibration, level splitting perturbation, crystal field splitting and the orthogonal group are also covered. Application-oriented solved problems and exercises are interspersed throughout the text to reinforce understanding of the key concepts.
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 1-108-55486-5
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