量子电动力学

　　片断：INTRODUCTION？1.TheuncertaintyprincipleintherelativisticcaseTHEquantumtheorydescribedinVolume3（QuantumMechanics）isessentiallynon-relativisticthroughout，andisnotapplicabletophenomenainvolvingmotionatvelocitiescomparablewiththatoflight.Atfirstsight，onemightexpectthatthechangetoarelativistictheoryispossiblebyafairlydirectgeneralizationoftheformalismofnon-relativisticquantummechanics.Butfurtherconsiderationshowsthatalogicallycompleterelativistictheorycannotbeconstructedwithoutinvokingnewphysicalprinciples.Letusrecallsomeofthephysicalconceptsformingthebasisofnon-relativisticquantummechanics（QM，？）.Wesawthatonefundamentalconceptisthatofmeasurement，bywhichismeanttheprocessofinteractionbetwecnaquantumsystemandaclassicalobjectorapparatus，causingthequantumsystemtoacquiredefinitevaluesofsomeparticulardynamicalvariables（coordinates，velocities，etc.）.Wesawalsothatquantummechanicsgreatlyrestrictsthepossibilitythatanelectrontsimultaneouslypossessesvaluesofdifferentdynamicalvariables.Forexample，theuncertaintiesAqandApinsimultaneouslyexistingvaluesofthecoordinateandthemomentumarerelatedbythecxpressiontqp~h;thegreatertheaccuracywithwhichoneofthesequantitiesismeasured，thelesstheaccuracywithwhichtheothercanbemeasuredatthesametime.Itisimportanttonote，however，thatanyofthedynamicalvariablesoftheelectroncanindividuallybemeasuredwitharbitrarilyhighaccuracy，andinanarbitrarilyshortperiodoftime.Thisfactisoffundamentalimportancethroughoutnon-relativisticquantummechanics.Itistheonlyjustificationforusingtheconceptofthewavefunction，whichisabasicpartofthcformalism.Thephysicalsignificanceofthewavefunction（q）isthatthesquareofitsmodulusgivestheprobabilityoffindingaparticularvalueoftheelectroncoordinateastheresultofameasurementmadeatagiveninstant.Theconceptofsuchaprobabilityclearlyrequiresthatthecoordinatecaninprinciplebemeasuredwithanyspecifiedaccuracyandrapidity，sinceotherwisethisconceptwouldbepurposelessanddevoidofphysicalsignificance.Theexistenceofalimitingvelocity（thevelocityoflight，denotedbyc）leadstonewfundamentallimitationsonthepossiblemeasurementsofvariousphysicalquantities（L.D.LandauandR.E.Peierls，1930）.InQM，？4，thefollowingrelationshiphasbeenderived：relatingtheuncertaintyApinthemeasurementoftheelectronmomentumandthedurationofthemeasurementprocessitself;vandv'arethevelocitiesoftheelectronbeforeandafterthemeasurement.Fromthisrelationshipitfollowsthatamomentummeasurementofhighaccuracymadeduringashorttime（i.e.withApandAtbothsmall）canoccuronlyifthereisalargechangeinthevelocityasaresultofthemeasurementprocessitself.Inthenon-relativistictheory，thisshowedthatthemeasurementofmomentumcannotberepeatedatshortintervalsoftime，butitdidnotatalldiminishthepossibility，inprinciple，ofmakingasinglemeasurementofthemomentumwitharbitrarilyhighaccuracy，sincethedifferencev'-vcouldtakeanyvalue，nomatterhowlarge.Theexistenceofalimitingvelocity，however，radicallyaltersthesituation.Thedifferencev'-v，likethevelocitiesthemselves，cannotnowexceedc（orrather2c）.Replacingv'-vin（l.1byc，weobtainwhichdeterminesthehighestaccuracytheoreticallyattainablewhenthemomen-tumismeasuredbyaprocessoccupyingagiventimet.Intherelativistictheory，therefore，itisinprincipleimpossibletomakeanarbitrarilyaccurateandrapidmeasurementofthemomentum.Anexactmeasurementispossibleonlyinthelimitasthedurationofthemeasurementtendstoinfinity.Thereisreasontosupposethattheconceptofmeasurabilityoftheelectroncoordinateitselfmustalsoundergomodification.Inthemathematicalformalismofthetheory，thissituationisshownbythefactthatanaccuratemeasurementofthecoordinateisincompatiblewiththeassertionthattheenergyofafreeparticleispositive.Itwillbeseenlaterthatthecompletesetofeigenfunctionsoftherelativisticwaveequationofafreeparticleincludes，aswellassolutionshavingthe"correct"timedependence，alsosolutionshavinga"negativefrequency".Thesefunctionswillingeneralappearinthecxpansionofthewavepacketcorrespondingtoanelectronlocalizedinasmallregionofspace.Itwillbeshownthatthewavefunctionshavinga"negativefrequency"correspondtotheexistenceofantiparticles（positrons）.Theappearanceofthesefunctionsintheexpansionofthewavepacketexpressesthe（ingeneral）inevitableproductionofelectron-positronpairsintheprocessofmeasuringthecoordinatesofanelectron.Thisformationofnewparticlesinawaywhichcannotbedetectedbytheprocessitselfrendersmeaninglessthemeasurementoftheelectroncoor-dinates.

暂缺《量子电动力学》作者简介

NOTATION.
INTRODUCTION
1.Theuncertaintyprincipleintherelativisticcase
I.PHOTONS
2.Quantizationofthefreeelectromagneticfield
3.Photons
4.Gaugeinvariance
5.Theelectromagneticfieldinquantumtheory
6.Theangularmomentumandparityofthephoton
7.Sphericalwavesofphotons
8.Thepolarizationofthephoton
9.Atwo-photonsystem
II.BOSONS
10.Thewaveequationforparticleswithspinzero
11.Particlesandantiparticles
12.Strictlyneutralparticles
13.ThetransformationsC,PandT
14.Thewaveequationforaparticlewithspinone
15.Thewaveequationforparticleswithhigherintegralspins
16.Helicitystatesofaparticle
III.FERMIONS
17.Four-dimensionalspinors
18.Therelationbetweenspinorsand4-vectors
19.Inversionofspinors
20.Dirac'sequationinthespinorrepresentation
21..ThesymmetricalformofDirac'sequation
22.AlgebraofDiracmatrices
23.Planewaves
24.Sphericalwaves
25.Therelationbetweenthespinandthestatistics
26.Chargeconjugationandtimereversalofspinors
27.Internalsymmetryofparticlesandantiparticles
28.Bilinearforms
29.Thepolarizationdensitymatrix
30.Neutrinos
31.Thewaveequationforaparticlewithspin3/2
IV.PARTICLESINANEXTERNALFIELD
32.Dirac'sequationforanelectroninanexternalfield
33.Expansioninpowersofllc
34.Finestructureoflevelsofthehydrogenatom
35.Motioninacentrallysymmetricfield
36.MotioninaCoulombfield
37.Scatteringinacentrallysymmetricfield
38.Scatteringintheultra-relativisticcase
39.Thecontinuous-spectrumwavefunctionsforscatteringinaCoulombfield
40.Anelectroninthefieldofanelectromagneticplanewave
41.Motionofspininanexternalfield
42.Neutronscatteringinanelectricfield
V.RADIATION
43.Theelectromagneticinteractionoperator
44.Emissionandabsorption
45.Dipoleradiation
46.Electricmultipoleradiation
47.Magneticmultipoleradiation
48.Angulardistributionandpolarizationoftheradiation
49.Radiationfromatoms:theelectrictype
50.Radiationfromatoms:themagnetictype
51.Radiationfromatoms:theZeemanandStarkeffects
52.Radiationfromatoms:thehydrogenatom
53.Radiationfromdiatomicmolecules:electronicspectra
54.Radiationfromdiatomicmolecules:vibrationalandrotationalspectra
55.Radiationfromnuclei
56.Thephotoelectriceffect:non-relativisticcase
57.Thephotoelectriceffect:relativisticcase
58.Photodisintegrationofthedeuteron
VI.SCATTERINGOFRADIATION
59.Thescatteringtensor
60.Scatteringbyfreelyorientedsystems
61.Scatteringbymolecules
62.Naturalwidthofspectrallines
63.Resonancefluorescence
VII.THESCATTERINGMATRIX
64.Thescatteringamplitude
65.Reactionsinvolvingpolarizedparticles
66.Kinematicinvariants
67.Physicalregions
68.Expansioninpartialamplitudes
69.Symmetryofhelicityscatteringamplitudes
70.Invariantamplitudes
71.Theunitaritycondition
VIII.INVARIANTPERTURBATIONTHEORY
72.Thechronologicalproduct
73.Feynmandiagramsforelectronscattering
74.Feynmandiagramsforphotonscattering
75.Theelectronpropagator
76.Thephotonpropagator
77.Generalrulesofthediagramtechnique..
78.Crossinginvariance
79.Virtualparticles
IX.INTERACTIONOFELECTRONS
80.Scatteringofanelectroninanexternalfield
81.Scatteringofelectronsandpositronsbyanelectron
82.Ionizationlossesoffastparticles
83.BreWsequation
84.Positronium
85.Theinteractionofatomsatlargedistances
X.INTERACTIONOFELECTRONSWITHPHOTONS
86.Scatteringofaphotonbyanelectron
87.Scatteringofaphotonbyanelectron.Polarizationeffects
88.Two-photonannihilationofanelectronpair
89.Annihilationofpositronium
90.Synchrotronradiation
91.Pairproductionbyaphotoninamagneticfield
92.Electron-nucleusbremsstrahlung.Thenon-relativisticcase
93.Electron-nucleusbremsstrahlung.Therelativisticcase
94.Pairproductionbyaphotoninthefieldofanucleus
95.Exacttheoryofpairproductionintheultra-relativisticcase
96.Exacttheoryofbremsstrahlungintheultra-relativisticcase
97.Electron-electronbremsstrahlungintheultra-relativisticcase
98.Emissionofsoftphotonsincollisions
99.Themethodofequivalentphotons
100.Pairproductionincollisionsbetweenparticles
101.Emissionofaphotonbyanelectroninthefieldofastrongelectromagneticwave
XI.EXACTPROPAGATORSANDVERTEXPARTS
102.FieldoperatorsintheHeisenbergrepresentation
103.Theexactphotonpropagator
104.Theself-energyfunctionofthephoton
105.Theexactelectronpropagator
106.Vertexparts
107.Dyson'sequations
108.Ward'sidentity
109.Electronpropagatorsinanexternalfield
110.Physicalconditionsforrenormalization
111.Analyticalpropertiesofphotonpropagators
112.RegularizationofFeynmanintegrals
XII.RADIATIVECORRECTIONS
113.Calculationofthepolarizationoperator
114.RadiativecorrectionstoCoulomb'slaw
115.CalculationoftheimaginarypartofthepolarizationoperatorfromtheFeynmanintegral
116.Electromagneticformfactorsoftheelectron
117.Calculationofelectronformfactors
118.Anomalousmagneticmomentoftheelectron
119.Calculationofthemassoperator
120.Emissionofsoftphotonswithnon-zeromass
121.ElectronscatteringinanexternalfieldinthesecondBornapproximation
122.Radiativecorrectionstoelectronscatteringinanexternalfield
123.Radiativeshiftofatomiclevels
124.Radiativeshiftofmesic-atomlevels
125.Therelativisticequationforboundstates
126.Thedoubledispersionrelation
127.Photon-photonscattering
128.Coherentscatteringofaphotoninthefieldofanucleus
129.Radiativecorrectionstotheelectromagneticfieldequations
130.Photonsplittinginamagneticfield
131.Calculationofintegralsoverfour-dimensionalregions
XIII.ASYMPTOTICFORMULAEOFQUANTUMELECTRODYNAMICS
132.Asymptoticformofthephotonpropagatorforlargemomenta
133.Therelationbetweenunrenormalizedandactualcharges
134.Asymptoticformofthescatteringamplitudesathighenergies
135.Separationofthedouble-logarithmictermsinthevertexoperator
136.Double-logarithmicasymptoticformofthevertexoperator
137.Double-logarithmicasymptoticformoftheelectron-muonscatteringamplitude
XIV.ELECTRODYNAMICSOFHADRONS
138.Electromagneticformfactorsofhadrons
139.Electron-hadronscattering
140.TheIow-energytheoremforbremsstrahlung
141.TheIow-energytheoremforphoton-hadronscattering
142.Multipolemomentsofhadrons
143.Inelasticelectron-hadronscattering
144.Hadronformationfromanelectron-positronpair
INDEX...