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[英] 彭罗斯 著 / 世界图书出版公司 / 2009-01 / 平装
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经典英文物理教材系列:旋量与时空(第1卷)
《旋量与时空(第1卷)》isthefirsttopresentacomprehensivedevelopmentofspace-timegeometryusingthe2-spinorformalism.Therearealsoseveralothernewfeaturesinourpresentation.Oneoftheseisthesystematicandconsistentuseoftheabstractindexapproachtotensorandspinorcalculus.Wehopethatthepuristdifferentialgeometerwhocasuallyleafsthroughthebookwillnotautomaticallybeputoffbytheappearanceofnumerousindices.Exceptfortheoccasionalbold-faceuprightones,ourindicesdifferfromthemoreusualonesinbeingabstractmarkerswithoutreferencetoanybasisorcoordinatesystem.Ouruseofabstractindicesleadstoanumberofsimplificationsoverconventionaltreatments.
Preface1Thegeometryofworld-vectorsandspin-vectors1.1Minkowskivectorspace1.2Nulldirectionsandspintransformations1.3SomepropertiesofLorentztransformations1.4Nullflagsandspin-vectors1.5Spinorialobjectsandspinstructure1.6Thegeometryofspinoroperations2Abstractindicesandspinoralgebra2.1Motivationforabstract-indexapproach2.2Theabstract-indexformalismfortensoralgebra2.3Bases2.4Thetotalreflexivityofonamanifold2.5Spinoralgebra3Spinorsandworid-tensors3.1World-tensorsasspinors3.2Nullflagsandcomplexnullvectors3.3Symmetryoperations3.4Tensorrepresentationofspinoroperations3.5Simplepropositionsabouttensorsandspinorsatapoint3.6Lorentztransformations4Differentiationandcurvature4.1Manifolds4.2Covariantderivative4.3Connection-independentderivatives4.4Differentiationofspinors4.5Differentiationofspinorcomponents4.6Thecurvaturespinors4.7SpinorformulationoftheEinstein-Cartan-Sciama-Kibbletheory4.8TheWeyltensorandtheBeI-Robinsontensor4.9Spinorformofcommutators4.10SpinorformoftheBianchiidentity4.11Curvaturespinorsandspin-coefficients4.12Compactedspin-coefficientformalism4.13Cartansmethod4.14Applicationsto2-surfaces4.15Spin-weightedsphericalharmonics5Fieldsinspace-time5.1Theelectromagneticfieldanditsderivativeoperator5.2Einstein-Maxwellequationsinspinorform5.3TheRainichconditions5.4Vectorbundles5.5Yang-Millsfields5.6Conformalrescalings5.7Masslessfields5.8Consistencyconditions5.9Conformalinvarianceofvariousfieldquantities5.10Exactsetsoffields5.11Initialdataonalightcone5.12ExplicitfieldintegralsAppendix:diagrammaticnotationReferencesSubjectandauthorindexIndexofsymbols
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