群论

图书标准信息

• 作者 Pierre Pamond 著
• 出版社 世界图书出版公司
• 出版时间 2014-09
• 版次 1
• ISBN 9787510078712
• 定价 79.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 310页
• 正文语种 简体中文

【内容简介】

　　《群论》旨在为物理学家介绍群理论的许多有趣的数学方面，同时将数学家带入物理应用。针对高年级本科生和研究生，书中给出了有限群和连续群的最全面的特点，并且强调在基础物理中的应用；展开讨论了有限群，重点强调了不可约表示和不变性；详细论述了李群，也用较多的笔墨讲述了Kac－Moody代数，包括Dynkin图。

【目录】

1Preface：thepursuitofsymmetries
2Finitegroups：anintroduction
2.1Groupaxioms
2.2Finitegroupsofloworder
2.3Permutations
2.4Basicconcepts
2.4.1Conjugation
2.4.2Simplegroups
2.4.3Sylow'scriteria
2.4.4Semi-directproduct
2.4.5YoungTableaux

3Finitegroups：representations
3.1Introduction
3.2Schur'slemmas
3.3The，，44charactertable
3.4Kroneckerproducts
3.5Realandcomplexrepresentations
3.6Embeddings
3.7Zncharactertable
3.8Dncharactertable
3.9Q2，charactertable
3.10Somesemi-directproducts
3.11Inducedrepresentations
3.12Invariants
3.13Coverings

4Hilbertspaces
4.1FiniteHilbertspaces
4.2Fermioscillators
4.3InfiniteHilbertspaces

5SU（2）
5.1Introduction
5.2Somerepresentations
5.3FromLiealgebrastoLiegroups
5.4SU（2）→SU（1，1）
5.5SelectedSU（2）applications
5.5.1Theisotropicharmonicoscillator
5.5.2TheBohratom
5.5.3Isotopicspin

6SU（3）
6.1SU（3）algebra
6.2α-Basis
6.3β-Basis
6.4α'-Basis
6.5Thetripletrepresentation
6.6TheChevalleybasis
6.7SU（3）inphysics
6.7.1Theisotropicharmonicoscillatorredux
6.7.2TheElliottmodel
6.7.3TheSakatamodel
6.7.4TheEightfoldWay

7ClassificationofcompactsimpleLiealgebras
7.1Classification
7.2Simpleroots
7.3Rank-twoalgebras
7.4Dynkindiagrams
7.5Orthonormalbases

8Liealgebras：representationtheory
8.1Representationbasics
8.2A3fundamentals
8.3TheWeylgroup
8.4OrthogonalLiealgebras
8.5Spinorrepresentations
8.5.1SO（2n）spinors
8.5.2SO（2n+1）spinors
8.5.3Cliffordalgebraconstruction
8.6CasimirinvariantsandDynkinindices
8.7Embeddings
8.8Oscillatorrepresentations
8.9Vermamodules
8.9.1Weyldimensionformula
8.9.2Vermabasis

9Finitegroups：theroadtosimplicity
9.1MatricesoverGaloisfields
9.1.1PSL2（7）
9.1.2Adoublytransitivegroup
9.2Chevalleygroups
9.3Afleetingglimpseatthesporadicgroups

10BeyondLiealgebras
10.1Serrepresentation
10.2AffineKac-Moodyalgebras
10.3Superalgebras

11ThegroupsoftheStandardModel
11.1Space-timesymmetries
11.1.1TheLorentzandPoincar6groups
11.1.2Theconformalgroup
11.2Beyondspace-timesymmetries
11.2.1Colorandthequarkmodel
11.3InvariantLagrangians
11.4Non-Abeliangaugetheories
11.5TheStandardModel
11.6GrandUnification
11.7Possiblefamilysymmetries
11.7.1FiniteSU（2）andSO（3）subgroups
11.7.2FiniteSU（3）subgroups

12Exceptionalstructures
12.1Hurwitzalgebras
12.2MatricesoverHurwitzalgebras
12.3TheMagicSquare
Appendix1Propertiesofsomefinitegroups
Appendix2PropertiesofselectedLiealgebras
References
Index