物理學家用的幾何代數

《物理學家用的幾何代數》是2014年9月1日世界圖書出版公司出版的圖書，作者是[英]C.多蘭（Chris Doran）。

基本介紹

• 中文名：物理學家用的幾何代數
• 作者：[英]C.多蘭（Chris Doran）
• 出版社：世界圖書出版公司
• 出版時間：2014年9月1日
• ISBN：9787510078552 

內容簡介

《物理學家用的幾何代數》是一部不僅讓對物理學感興趣的讀者的讀物，也是一本對物理現實感興趣的讀者的讀物。幾何代數在過去的十年中得到了快速發展，成為物理和工程領域的一個重要課題。作者是該領域的一個領頭人物，做了許多重大進展。書中帶領讀者走進該領域，其中包括好多套用，黑洞物理學和量子計算，非常適於作為一本幾何代數物理套用方面的研究生教程。

目錄

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