Group Theoretical Methods and Their Applications

AvE. Stiefel,A. Fässler

Häftad, Engelska, 2012

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x system Ib-TEX. I wish to thank her for the beautiful work and the numerous discussions on the contents of this book. I am indebted to Peter Fassler, Neu-Technikum Buchs, Switzerland, for drafting the figures, to my students Kurt Rothermann and Stefan Strahl for computer enhancing and labeling the graphics, to Pascal Felder and Markus Wittwer for a simulation program that generated the figures in the stochastics sections. My thanks go to my new colleague at work, Daniel Neuenschwander, for the inspiring discussions related to the section in stochastics and for reading the manuscript to it. I am also grateful to Dacfey Dzung for reading the whole manuscript. Thanks go especially to Professor \Valter Gander of ETH, Zurich, who at the finishing stage and as an expert of 'JEXgenerously invested numerous hours to assist us in solving software as well as hardware problems; thanks go also to Martin Muller, Ingenieurschule Biel, who made the final layout of this book on the NeXT computer.Thanks are also due to Helmut Kopka of the Max Planck Institute, for solving software problems, and to Professor Burchard Kaup of the Uni- versity of Fribourg, Switzerland for adding some useful software; also to Birkhauser Boston Inc. for the pleasant co-operation. Finally, let me be reminiscent of Professor E. Stiefel (deceased 1978) with whom I had many interesting discussions and true co-operation when writing the book in German.

Produktinformation

Utgivningsdatum:2012-09-30
Mått:210 x 279 x 17 mm
Vikt:765 g
Format:Häftad
Språk:Engelska
Antal sidor:296
Förlag:Springer-Verlag New York Inc.
ISBN:9781461267423

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Innehållsförteckning

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.