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＜電子ブック＞
Group Theoretical Methods and Their Applications / by E. Stiefel, A. Fässler

版	1st ed. 1992.
出版者	Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser
出版年	1992
本文言語	英語
大きさ	XII, 296 p : online resource
冊子体	Group theoretical methods and their applications / A. Fässler, E. Stiefel ; with English translation by Baoswan Dzung Wong ; : us,: sz
著者標目	*Stiefel, E author Fässler, A author SpringerLink (Online service)
件　名	LCSH:Group theory LCSH:Algebra LCSH:Mathematics FREE:Group Theory and Generalizations FREE:Algebra FREE:Applications of Mathematics
一般注記	1 Preliminaries -- 1.1 The Concept of Groups -- 1.2 Price Index in Economics -- 1.3 The Realization of Groups -- 1.4 Representation of Groups -- 1.5 Equivalence of Representations -- 1.6 Reducibility of Representations -- 1.7 Complete Reducibility -- 1.8 Basic Conclusions -- 1.9 Representations of Special Finite Groups -- 1.10 Kronecker Products -- 1.11 Unitary Representations -- Problems -- 2 Linear Operators with Symmetries -- 2.1 Schur’s Lemma -- 2.2 Symmetry of a Matrix -- 2.3 The Fundamental Theorem -- Problems -- 3 Symmetry Adapted Basis Functions -- 3.1 Illustration by Dihedral Groups -- 3.2 Application in Quantum Physics -- 3.3 Application to Finite Element Method -- 3.4 Perturbed Problems with Symmetry -- 3.5 Fast Fourier Transform on Finite Groups -- 4 Continuous Groups And Representations -- 4.1 Continuous Matrix Groups -- 4.2 Relationship Between Some Groups -- 4.3 Constructing Representations -- 4.4 Clebsch-Gordan Coefficients -- 4.5 The Lorentz group and SL(2,C) -- Problems -- 5 Symmetry Ad. Vectors, Characters -- 5.1 Orthogonality of Representations -- 5.2 Algorithm for Symmetry Adapted Bases -- 5.3 Applications -- 5.4 Similarity Classes of Groups -- 5.5 Characters -- 5.6 Representation Theory of Finite Groups -- 5.7 Extension to Compact Lie Groups -- Problems -- 6 Various Topics of Application -- 6.1 Bifurcation and A New Technique -- 6.2 A Diffusion Model in Probability Theory -- Problems -- 7 Lie Algebras -- 7.1 Infinitesimal Operator and Exponential Map -- 7.2 Lie Algebra of a Continuous Group -- 7.3 Representation of Lie Algebras -- 7.4 Representations of SU(2) and SO(3) -- 7.5 Examples from Quantum Mechanics -- Problems -- 8 Applications to Solid State Physics -- 8.1 Lattices -- 8.2 Point Groups and Representations -- 8.3 The 32 Crystal Classes -- 8.4 Symmetries and the Ritz Method -- 8.5 Examples ofApplications -- 8.6 Crystallographic Space Groups -- Problems -- 9 Unitary and Orthogonal Groups -- 9.1 The Groups U(n) and SU(n) -- 9.2 The Special Orthogonal Group SO(n) -- 9.3 Subspaces of Representations of SU(3) -- A -- Answers to Selected Problems Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-0395-7

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