Quantum statistical field theory : an introduction to Schwinger’s variational method with Green’s function nanoapplication, graphene and superconductivity

453 Pages·2017·4.885 MB·English

by  Horing, Norman J. M.

INTERNATIONAL SERIES OF MONOGRAPHS
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INTERNATIONAL SERIES OF MONOGRAPHS ON PHYSICS
166.N.Horing:Quantumstatisticalfieldtheory
165.T.C.Choy:Effectivemediumtheory,Secondedition
164.L.Pitaevskii,S.Stringari:Bose-Einsteincondensationandsuperfluidity
163.B.J.Dalton,J.Jeffers,S.M.Barnett:Phasespacemethodsfordegeneratequantumgases
162.W.D.McComb:Homogeneous,isotropicturbulence-phenomenology,renormalizationandstatisticalclosures
161.V.Z.Kresin,H.Morawitz,S.A.Wolf:Superconductingstate-mechanismsandproperties
160.C.Barrabès,P.A.Hogan:Advancedgeneralrelativity-gravitywaves,spinningparticles,andblackholes
159.W.Barford:Electronicandopticalpropertiesofconjugatedpolymers,Secondedition
158.F.Strocchi:Anintroductiontonon-perturbativefoundationsofquantumfieldtheory
157.K.H.Bennemann,J.B.Ketterson:Novelsuperfluids,Volume2
156.K.H.Bennemann,J.B.Ketterson:Novelsuperfluids,Volume1
155.C.Kiefer:Quantumgravity,Thirdedition
154.L.Mestel:Stellarmagnetism,Secondedition
153.R.A.Klemm:Layeredsuperconductors,Volume1
152.E.L.Wolf:Principlesofelectrontunnelingspectroscopy,Secondedition
151.R.Blinc:Advancedferroelectricity
150.L.Berthier,G.Biroli,J.-P.Bouchaud,W.vanSaarloos,L.Cipelletti:Dynamicalheterogeneitiesinglasses,colloids,and
granularmedia
149.J.Wesson:Tokamaks,Fourthedition
148.H.Asada,T.Futamase,P.Hogan:Equationsofmotioningeneralrelativity
147.A.Yaouanc,P.DalmasdeRéotier:Muonspinrotation,relaxation,andresonance
146.B.McCoy:Advancedstatisticalmechanics
145.M.Bordag,G.L.Klimchitskaya,U.Mohideen,V.M.Mostepanenko:AdvancesintheCasimireffect
144.T.R.Field:Electromagneticscatteringfromrandommedia
143.W.Götze:Complexdynamicsofglass-formingliquids-amode-couplingtheory
142.V.M.Agranovich:Excitationsinorganicsolids
141.W.T.Grandy:Entropyandthetimeevolutionofmacroscopicsystems
140.M.Alcubierre:Introductionto3+1numericalrelativity
139.A.L.Ivanov,S.G.Tikhodeev:Problemsofcondensedmatterphysics-quantumcoherencephenomenainelectron-holeand
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138.I.M.Vardavas,F.W.Taylor:Radiationandclimate
137.A.F.Borghesani:Ionsandelectronsinliquidhelium
135.V.Fortov,I.Iakubov,A.Khrapak:Physicsofstronglycoupledplasma
134.G.Fredrickson:Theequilibriumtheoryofinhomogeneouspolymers
133.H.Suhl:Relaxationprocessesinmicromagnetics
132.J.Terning:Modernsupersymmetry
131.M.Mariño:Chern-Simonstheory,matrixmodels,andtopologicalstrings
130.V.Gantmakher:Electronsanddisorderinsolids
129.W.Barford:Electronicandopticalpropertiesofconjugatedpolymers
128.R.E.Raab,O.L.deLange:Multipoletheoryinelectromagnetism
127.A.Larkin,A.Varlamov:Theoryoffluctuationsinsuperconductors
126.P.Goldbart,N.Goldenfeld,D.Sherrington:Stealingthegold
125.S.Atzeni,J.Meyer-ter-Vehn:Thephysicsofinertialfusion
123.T.Fujimoto:Plasmaspectroscopy
122.K.Fujikawa,H.Suzuki:Pathintegralsandquantumanomalies
121.T.Giamarchi:Quantumphysicsinonedimension
120.M.Warner,E.Terentjev:Liquidcrystalelastomers
119.L.Jacak,P.Sitko,K.Wieczorek,A.Wojs:Quantumhallsystems
117.G.Volovik:TheUniverseinaheliumdroplet
116.L.Pitaevskii,S.Stringari:Bose-Einsteincondensation
115.G.Dissertori,I.G.Knowles,M.Schmelling:Quantumchromodynamics
114.B.DeWitt:Theglobalapproachtoquantumfieldtheory
113.J.Zinn-Justin:Quantumfieldtheoryandcriticalphenomena,Fourthedition
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106.J.Kübler:Theoryofitinerantelectronmagnetism
105.Y.Kuramoto,Y.Kitaoka:Dynamicsofheavyelectrons
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103.G.C.Branco,L.Lavoura,J.P.Silva:CPViolation
101.H.Araki:Mathematicaltheoryofquantumfields
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Quantum Statistical Field Theory
An Introduction to Schwinger’s Variational Method
with Green’s Function Nanoapplications, Graphene
and Superconductivity
Norman J. Morgenstern Horing
DepartmentofPhysicsandEngineeringPhysics,StevensInstituteofTechnology
3
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RoseMorgensternHoring
1911–1999
Deeplylovedmotherandprotectorwho,intheworstoftimes,bravedsevereadversity
andprivationtodelivermetomanhood
NormanJ.MorgensternHoring

Contents
Prologue xiii
Acknowledgments xvii
1 DiracNotationandTransformationTheory 1
1.1 IntroductoryReview 1
1.2 DiracNotation 8
1.3 CompleteSetsofCommutingObservables,Representationsand
TransformationTheory 13
1.4 SchwingerMeasurementSymbols 15
1.5 Chapter1Problems 16
1.6 ReferencesforChapter1 19
2 Identical Particles and Second Quantization: Occupation
NumberRepresentation 20
2.1 OperatorsforPropertiesofIdenticalParticles 20
2.2 SecondQuantization:OccupationNumberRepresentation 24
2.3 CoherentStates,SqueezedStates 33
2.4 Chapter2Problems 38
2.5 ReferencesforChapter2 39
3 Q. M. Pictures; Heisenberg Equation; Linear Response;
SuperoperatorsandNon-MarkovianEquations 40
3.1 SchrödingerPicture:IterationSeriesfortheTime-DevelopmentOperator 41
3.2 HeisenbergPictureandEquationsofMotion 44
3.3 InteractionPicture 47
3.4 LinearResponse 51
3.5 S-Matrix,DensityMatrix,SuperoperatorsandNon-Markovian
KineticEquations 53
3.6 Chapter3Problems 59
3.7 ReferencesforChapter3 60
4 SchwingerActionPrincipleandVariationalCalculus 61
4.1 ActionPrinciple:QuantumHamiltonEquations 61
4.2 VariationalCalculusandSources 72
4.3 ParticleSources:GeneralConsiderations 81
4.4 PotentialSource:GeneralConsiderations 87
viii Contents
4.5 AnIdentity 91
4.6 Chapter4Problems 93
4.7 ReferencesforChapter4 93
5 RetardedGreen’sFunctions 95
5.1 Definition, Equation of Motion and Interpretation of Retarded
Green’sFunctions 95
5.2 PartialGreen’sFunctions,ApplicationstoLocalizedStatesina
ContinuumandChemisorption 101
5.3 DysonIntegralEquation,T-Matrixforδ(x)-FunctionPotential 105
5.4 RandomImpurityScattering:BornandSelf-ConsistentBorn
Approximations 107
5.5 Ando’sSemi-EllipticDensityofStatesforthe2D
Landau-QuantizedElectron-ImpuritySystem 113
5.6 MagneticFieldGreen’sFunctionforElectronsinThreeand
TwoDimensions 116
5.7 Green’s Function Determination by Hamilton Equations:
2DSaddlePotentialinE(t)Field 123
5.8 Product Green’s Functions for Separable Hamiltonians:
1DSuperlatticeinAxialFields 127
5.9 ElectronPropagationinaHeterostructurewithSpatiallyVariable
Mass:Green’sFunctionMatching 133
5.10 Green’sFunctionMatching:Dynamic,Non-LocalElectrostatic
ScreeningatInterface;SurfacePlasmons 138
5.11 FeynmanPathIntegrals 144
5.12 Chapter5Problems 145
5.13 ReferencesforChapter5 148
6 Quantum Mechanical Ensemble Averages and Statistical
Thermodynamics 150
6.1 QuantumMechanicalEnsembleAveragesandThermodynamics 150
6.2 BosonandFermionStatisticsforNon-InteractingSystems:Bose
Condensation 156
6.3 HelmholtzFreeEnergyandMagneticMoment 159
6.4 DiamagneticSusceptibilityandthedeHaas–vanAlphenEffect 163
6.5 Chapter6Problems 166
6.6 ReferencesforChapter6 167
7 ThermodynamicGreen’sFunctionsandSpectralStructure 168
7.1 DefinitionandInterpretationofThermalGreen’sFunctions 168
7.2 LehmannSpectralRepresentationoftheOne-ParticleThermal
Green’sFunction 169
7.3 OtherSpectralConsiderations 173
7.4 Periodicity/Antiperiodicity in Imaginary Time, Matsubara
FrequenciesandAnalyticContinuation 174
Contents ix
7.5 Commutator/Anticommutator Functions;
Retarded/Advanced Green’s Functions;
SpectralSumRule 179
7.6 Statistical Thermodynamic Information in the One-
andTwo-ParticleGreen’sFunctions 182
7.7 Chapter7Problems 185
7.8 ReferencesforChapter7 186
8 EquationsofMotionwithParticle–ParticleInteractions
andApproximations 187
8.1 MultiparticleGreen’sFunctionEquationsofMotion 188
8.2 Non-Correlation Decoupling Procedures for G : Hartree and
2
Hartree–FockApproximations 191
8.3 Non-CorrelationDecouplingProcedures:CollisionalEffects;Sum
ofLadderDiagramsIntegralEquation 195
8.4 Electron–HoleInteraction:ExcitonStates 198
8.5 Chapter8Problems 204
8.6 ReferencesforChapter8 205
9 Non-Equilibrium Green’s Functions: Variational Relations
andApproximationsforParticleInteractions 206
9.1 Non-Equilibrium Green’s Functions, Definitions
andVariationalRelationsinTermsofParticleSources 207
9.2 Exact Variational Relations in Terms
ofaSourcePotential 216
9.3 CumulantsandtheLinkedClusterTheorem 218
9.4 Variational Differential Formulation
oftheRandomPhaseApproximation 221
9.5 Variational Differential Formulation
ofPerturbationTheory 225
9.6 Self-EnergyandVertexOperatorPerturbationTheory 227
9.7 ShieldedPotentialPerturbationTheory 229
9.8 ImaginaryTime,ContourTimeOrderingandtheLangrethAlgebra 231
9.9 GeneralizedKadanoff–BaymAnsatzforDerivationofQuantum
TransportEquations 234
9.10 Chapter9Problems 236
9.11 ReferencesforChapter9 237
10 Random Phase Approximation Plasma Phenomenology,
SemiclassicalandHydrodynamicModels;Electrodynamics 238
10.1 Dielectric Response Functions for Inhomogeneous
andHomogeneousSystems 239
10.2 RPA Plasmons and Shielding in 3D, 2D and 1D,
Magnetoplasmas,ModelsandSurfacePlasmons 244
10.3 ExchangeandCorrelationEnergy 252