Group Theoretical Methods and Their Applications

Main Authors: Fässler, Albert, Stiefel, Eduard (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA Birkhäuser Boston 1992, 1992
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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 of Applications
  • 8.6 Crystallographic Space Groups
  • Problems
  • 9 Unitary and Orthogonal Groups
  • 9.1 The Groups U(n) and SU(n)
  • 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)
  • 9.2 The Special Orthogonal Group SO(n)
  • 9.3 Subspaces of Representations of SU(3)
  • A
  • Answers to Selected Problems