物理学家用的几何代数

图书标准信息

• 作者 [英]C.多兰（Chris Doran） 著
• 出版社 世界图书出版公司
• 出版时间 2014-09
• 版次 1
• ISBN 9787510078552
• 定价 149.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 578页
• 正文语种 英语

【内容简介】

　　《物理学家用的几何代数》是一部不仅让对物理学感兴趣的读者的读物，也是一本对物理现实感兴趣的读者的读物。几何代数在过去的十年中得到了快速发展，成为物理和工程领域的一个重要课题。作者是该领域的一个领头人物，做了许多重大进展。书中带领读者走进该领域，其中包括好多应用，黑洞物理学和量子计算，非常适于作为一本几何代数物理应用方面的研究生教程。

【目录】

Preface
Notation
1Introduction
1.1Vector（linear）spaces
1.2Thescalarproduct
1.3Complexnumbers
1.4Quaternions
1.5Thecrossproduct
1.6Theouterproduct
1.7Notes
1.8Exercises

2Geometricalgebraintwoandthreedimensions
2.1Anewproductforvectors
2.2Anoutlineofgeometricalgebra
2.3Geometricalgebraoftheplane
2.4Thegeometricalgebraofspace
2.5Conventions
2.6Reflections
2.7Rotations
2.8Notes
2.9Exercises

3Classicalmechanics
3.1Elementaryprinciples
3.2Two—bodycentralforceinteractions
3.3Celestialmechanicsandperturbations
3.4Rotatingsystemsandrigid—bodymotion
3.5Notes
3.6Exercises

4Foundationsofgeometricalgebra
4.1Axiomaticdevelopment
4.2Rotationsandrefiections
4.3Bases，framesandcomponents
4.4Linearalgebra
4.5Tensorsandcomponents
4.6Notes
4.7Exercises

5Relativityandspacetime
5.1Analgebraforspacetime
5.2Observers，trajectoriesandframes
5.3Lorentztransformations
5.4TheLorentzgroup
5.5Spacetimedynamics
5.6Notes
5.7Exercises

6Geometriccalculus
6.1Thevectorderivative
6.2Curvilinearcoordinates
6.3Analyticfunctions
6.4Directedintegrationtheory
6.5Embeddedsurfacesandvectormanifolds
6.6Elasticity
6.7Notes
6.8Exercises

7Classicalelectrodynamics
7.1Maxwell'sequations
7.2Integralandconservationtheorems
7.3Theelectromagneticfieldofapointcharge
7.4Electromagneticwaves
7.5Scatteringanddiffraction
7.6Scattering
7.7Notes
7.8Exercises

8Quantumtheoryandspinors
8.1Non—relativisticquantumspin
8.2Relativisticquantumstates
8.3TheDiracequation
8.4Centralpotentials
8.5Scatteringtheory
8.6Notes
8.7Exercises

9Multiparticlestatesandquantumentanglement
9.1Many—bodyquantumtheory
9.2Multiparticlespacetimealgebra
9.3Systemsoftwoparticles
9.4Relativisticstatesandoperators
9.5Two—spinorcalculus
9.6Notes
9.7Exercises

10Geometry
10.1Projectivegeometry
10.2Conformalgeometry
10.3Conformaltransformations
10.4Geometricprimitivesinconformalspace
10.5Intersectionandreflectioninconformalspace
10.6Non—Euclideangeometry
10.7Spacetimeconformalgeometry
10.8Notes
10.9Exercises

11Furthertopicsincalculusandgrouptheory
11.1Multivectorcalculus
11.2Grassmanncalculus
11.3Liegroups
11.4Complexstructuresandunitarygroups
11.5Thegenerallineargroup
11.6Notes
11.7Exercises

12LagrangianandHamiltoniantechniques
12.1TheEuler—Lagrangeequations
12.2Classicalmodelsforspin—1／2particles
12.3Hamiltoniantechniques
12.4Lagrangianfieldtheory
12.5Notes
12.6Exercises

13Symmetryandgaugetheory
13.1Conservationlawsinfieldtheory
13.2Electromagnetism
13.3Diractheory
13.4Gaugeprinciplesforgravitation
13.5Thegravitationalfieldequations
13.6ThestructureoftheRiemanntensor
13.7Notes
13.8Exercises

14Gravitation
14.1Solvingthefieldequations
14.2Spherically—symmetricsystems
14.3Schwarzschildblackholes
14.4Quantummechanicsinablackholebackground
14.5Cosmology
14.6Cylindricalsystems
14.7Axially—symmetricsystems
14.8Notes
14.9Exercises
Bibliography
Index