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1.

電子ブック

EB
Shoon K. Kim
出版情報:   1 online resource (xvi, 492 pages)
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目次情報: 続きを見る
Preface
List of symbols
Linear transformations / 1:
Theory of matrix transformations / 2:
Elements of abstract group theory / 3:
Unitary and orthogonal groups / 4:
The point groups of finite order / 5:
Theory of group representations / 6:
Construction of symmetry adapted linear combinations based on the correspondence theorem / 7:
Subduced and induced representations / 8:
Elements of continuous groups / 9:
The representations of the rotation group / 10:
Single- and double-valued representations of point groups / 11:
Projective representations / 12:
230 space groups / 13:
The representations of space groups / 14:
The unirreps of the space groups to energy bands and vibrational modes of crystals / 15:
Time reversal, antiunitary point groups and their core presentations / 16:
Antiunitary space groups and their core presentations / 17:
Appendix: Character tables for the crystal point groups
References
Character tables for the crystal point groups / Appendix:
Appendix
Preface
List of symbols
Linear transformations / 1:
2.

電子ブック

EB
Robert Gilmore
出版情報:   1 online resource (xi, 319 pages)
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Introduction / 1:
Lie groups / 2:
Matrix groups
Lie algebras / 4:
Matrix algebras / 5:
Operator algebras / 6:
Exponentiation / 7:
Structure theory for Lie algebras / 8:
Structure theory for simple Lie algebras / 9:
Root spaces and Dykin diagrams / 10:
Real forms / 11:
Riemannian symmetric spaces / 12:
Contraction / 13:
Hydrogenic atoms / 14:
Maxwell's equations / 15:
Lie groups and differential equations / 16:
References
Index
Preface
The program of Lie / 1.1:
A result of Galois / 1.2:
Group theory background / 1.3:
Approach to solving polynomial equations / 1.4:
Solution of the quadratic equation / 1.5:
Solution of the cubic equation / 1.6:
Solution of the quartic equation / 1.7:
The quintic cannot be solved / 1.8:
Example / 1.9:
Conclusion / 1.10:
Problems / 1.11:
Algebraic properties / 2.1:
Topological properties / 2.2:
Unification of algebra and topology / 2.3:
Unexpected simplification / 2.4:
Preliminaries / 2.5:
No constraints / 3.2:
Linear constraints / 3.3:
Bilinear and quadratic constraints / 3.4:
Multilinear constraints / 3.5:
Intersections of groups / 3.6:
Embedded groups / 3.7:
Modular groups / 3.8:
Why bother? / 3.9:
How to linearize a Lie group / 4.2:
Inversion of the linearization map: EXP / 4.3:
Properties of a Lie algebra / 4.4:
Structure constants / 4.5:
Regular representation / 4.6:
Structure of a Lie algebra / 4.7:
Inner product / 4.8:
Invariant metric and measure on a Lie group / 4.9:
Algebras of embedded groups / 4.10:
Basis vectors / 5.8:
Boson operator algebras / 5.10:
Fermion operator algebras / 6.2:
First order differential operator algebras / 6.3:
EXPonentiation / 6.4:
The covering problem / 7.1:
The isomorphism problem and the covering group / 7.3:
The parameterization problem and BCH formulas / 7.4:
EXPonentials and physics / 7.5:
Some standard forms for the regular representation / 7.6:
What these forms mean / 8.3:
How to make this decomposition / 8.4:
An example / 8.5:
Objectives of this program / 8.6:
Eigenoperator decomposition - secular equation / 9.2:
Rank / 9.3:
Invariant operators / 9.4:
Regular elements / 9.5:
Semisimple Lie algebras / 9.6:
Canonical commutation relations / 9.7:
Root spaces and Dynkin diagrams / 9.8:
Properties of roots / 10.1:
Root space diagrams / 10.2:
Dynkin diagrams / 10.3:
Compact and least compact real forms / 10.4:
Cartan's procedure for constructing real forms / 11.3:
Real forms of simple matrix Lie algebras / 11.4:
Results / 11.5:
Brief review / 11.6:
Globally symmetric spaces / 12.2:
Metric and measure / 12.3:
Applications and examples / 12.6:
Pseudo-Riemannian symmetric spaces / 12.7:
Inonu-Wigner contractions / 12.8:
Simple examples of Inonu-Wigner contractions / 13.3:
The contraction U(2) to H[subscript 4] / 13.4:
Two important principles of physics / 13.5:
The wave equations / 14.3:
Quantization conditions / 14.4:
Geometric symmetry SO(3) / 14.5:
Dynamical symmetry SO(4) / 14.6:
Relation with dynamics in four dimensions / 14.7:
DeSitter symmetry SO(4, 1) / 14.8:
Conformal symmetry SO(4, 2) / 14.9:
Spin angular momentum / 14.10:
Spectrum generating group / 14.11:
Maxwell's equations / 14.12:
Review of the inhomogeneous Lorentz group / 15.1:
Subgroups and their representations / 15.3:
Representations of the Poincare group / 15.4:
Transformation properties / 15.5:
The simplest case / 15.6:
First order equations / 16.2:
Additional insights / 16.3:
Bibliography / 16.5:
Introduction / 1:
Lie groups / 2:
Matrix groups
3.

電子ブック

EB
Derek F. Holt, University of Warwick, Sarah Rees, University of Newcastle upon Tyne, Claas E. Röver, National University of Ireland, Galway
出版情報:   1 online resource (xi, 294 pages)
シリーズ名: London Mathematical Society student texts ; 88
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4.

電子ブック

EB
Thomas Wolfram, Şinasi Ellialtioğlu
出版情報:   1 online resource (xii, 471 pages)
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目次情報:
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