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[英]C.多兰(Chris Doran) 著 / 世界图书出版公司 / 2014-09 / 平装
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物理学家用的几何代数
《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。
PrefaceNotation1Introduction1.1Vector(linear)spaces1.2Thescalarproduct1.3Complexnumbers1.4Quaternions1.5Thecrossproduct1.6Theouterproduct1.7Notes1.8Exercises2Geometricalgebraintwoandthreedimensions2.1Anewproductforvectors2.2Anoutlineofgeometricalgebra2.3Geometricalgebraoftheplane2.4Thegeometricalgebraofspace2.5Conventions2.6Reflections2.7Rotations2.8Notes2.9Exercises3Classicalmechanics3.1Elementaryprinciples3.2Two—bodycentralforceinteractions3.3Celestialmechanicsandperturbations3.4Rotatingsystemsandrigid—bodymotion3.5Notes3.6Exercises4Foundationsofgeometricalgebra4.1Axiomaticdevelopment4.2Rotationsandrefiections4.3Bases,framesandcomponents4.4Linearalgebra4.5Tensorsandcomponents4.6Notes4.7Exercises5Relativityandspacetime5.1Analgebraforspacetime5.2Observers,trajectoriesandframes5.3Lorentztransformations5.4TheLorentzgroup5.5Spacetimedynamics5.6Notes5.7Exercises6Geometriccalculus6.1Thevectorderivative6.2Curvilinearcoordinates6.3Analyticfunctions6.4Directedintegrationtheory6.5Embeddedsurfacesandvectormanifolds6.6Elasticity6.7Notes6.8Exercises7Classicalelectrodynamics7.1Maxwell'sequations7.2Integralandconservationtheorems7.3Theelectromagneticfieldofapointcharge7.4Electromagneticwaves7.5Scatteringanddiffraction7.6Scattering7.7Notes7.8Exercises8Quantumtheoryandspinors8.1Non—relativisticquantumspin8.2Relativisticquantumstates8.3TheDiracequation8.4Centralpotentials8.5Scatteringtheory8.6Notes8.7Exercises9Multiparticlestatesandquantumentanglement9.1Many—bodyquantumtheory9.2Multiparticlespacetimealgebra9.3Systemsoftwoparticles9.4Relativisticstatesandoperators9.5Two—spinorcalculus9.6Notes9.7Exercises10Geometry10.1Projectivegeometry10.2Conformalgeometry10.3Conformaltransformations10.4Geometricprimitivesinconformalspace10.5Intersectionandreflectioninconformalspace10.6Non—Euclideangeometry10.7Spacetimeconformalgeometry10.8Notes10.9Exercises11Furthertopicsincalculusandgrouptheory11.1Multivectorcalculus11.2Grassmanncalculus11.3Liegroups11.4Complexstructuresandunitarygroups11.5Thegenerallineargroup11.6Notes11.7Exercises12LagrangianandHamiltoniantechniques12.1TheEuler—Lagrangeequations12.2Classicalmodelsforspin—1/2particles12.3Hamiltoniantechniques12.4Lagrangianfieldtheory12.5Notes12.6Exercises13Symmetryandgaugetheory13.1Conservationlawsinfieldtheory13.2Electromagnetism13.3Diractheory13.4Gaugeprinciplesforgravitation13.5Thegravitationalfieldequations13.6ThestructureoftheRiemanntensor13.7Notes13.8Exercises14Gravitation14.1Solvingthefieldequations14.2Spherically—symmetricsystems14.3Schwarzschildblackholes14.4Quantummechanicsinablackholebackground14.5Cosmology14.6Cylindricalsystems14.7Axially—symmetricsystems14.8Notes14.9ExercisesBibliographyIndex
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开播时间:09月02日 10:30