AuthorFรคssler, Albert. author
TitleGroup Theoretical Methods and Their Applications [electronic resource] / by Albert Fรคssler, Eduard Stiefel
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1992
Connect tohttp://dx.doi.org/10.1007/978-1-4612-0395-7
Descript XII, 296 p. online resource

CONTENT

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 Schurโs 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 of Applications -- 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


SUBJECT

  1. Mathematics
  2. Algebra
  3. Group theory
  4. Applied mathematics
  5. Engineering mathematics
  6. Mathematics
  7. Group Theory and Generalizations
  8. Algebra
  9. Applications of Mathematics