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统计场论（第1卷）

统计场论（第1卷）
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作者: 编 , 编
出版社: 世界图书出版公司
2004-11
版次: 1
ISBN: 9787506266420
定价: 72.00
装帧: 平装
开本: 24开
纸张: 胶版纸
页数: 403页
分类: 自然科学
26人买过
  • Sometenyearsago,whencompletingwithJ.-B.ZuberaprevioustextonQuantumFieldTheory,theseniorauthorwaspainfullyawarethatlittlementionwasmadethatmethodsinstatisticalphysicsandEuclideanfieldtheorywerecomingcloserandcloser,withcommontoolsbasedontheuseofpathintegralsandtherenormalizationgroupgivinginsightsonglobalstructures.Itwaspartlytofillthisgapthatthepresentbookwasundertaken.Alas,overthefiveyearsthatittooktocometolife,bothsubjectshaveundergoneanewevolution.Disorderedmedia,growthpatterns,complexdynamicalsystemsorspinglassesareamongthenewimportanttopicsinstatisticalmechanics,whilesuperstringtheoryhasturnedtothestudyofextendedsystems,Kaluza-Kleintheoriesinhigherdimensions,anticommutingcoordinates...inanattempttoformulateaunifiedmodelincludingallknowninteractions.Newandsophisticatedtechniqueshaveinvadedstatisticalphysics,rangingfromalgebraicmethodsinintegrablesystemstofractalsetsorrandomsurfaces.Powerfulcomputersorspecialdevicesprovide"experimental"meansforanewbrandoftheoreticalphysicists.Inquantumfieldtheory,applicationsofdifferentialtopology,geometry,Riemannianmanifolds,operatortheory...requireadeeperbackgroundinmathematicsandaknowledgeofsomeofitsmostrecentdevelopments.Asaresult,whensurveyingwhathasbeenincludedinthepresentvolumeinanattempttouncoverthebasicunityofthesesubjects,theauthorshavethesameunsatisfactoryfeelingofnotbeingabletobringthereaderreallyuptodate.Itispresumablythefateofsuchendeavourstoalwayscomeshortofaccomplishingtheirpurpose. ContentsofVolume2
    Preface
    1FromBrownianmotiontoEuclideanfields
    1.1Brownianmotion
    1.1.1Randomwalks
    1.1.2Thesumoverpaths
    1.1.3ThedimensiontwoofBrowniancurves
    1.2Euclideanfields
    1.2.1Freefields
    1.2.2Interactingfieldsandrandomwalks
    1.2.3Self-avoidingwalksandthelimitn→0
    1.2.4Comparisonwiththehightemperatureexpansion
    1.2.5Theone-dimensionalcase
    1.ALattices
    Notes

    2Grassmannianintegralsandthetwo-dimensionalIsingmodel
    2.1Grassmannianintegrals
    2.1.1Anticommutingvariables
    2.1.2Integrals
    2.2Thetwo-dimensionalIsingmodel
    2.2.1Duality
    2.2.2Transfermatrix
    2.2.3Fermionicrepresentation
    2.2.4Freeenergy
    2.2.5Spontaneousmagnetization
    2.2.6Correlationfunctioninthehightemperaturephase
    2.2.7Surfacetension
    2.3Criticalcontinuoustheory
    2.3.1Effectiveaction
    2.3.2Correlationfunctions
    2.AQuadraticdifferencesandPainleveequationsNotes

    3Spontaneoussymmetrybreaking,meanfield
    3.1Meanfieldapproximation
    3.1.1Dielectriccoastantofapolarizablemedium
    3.1.2Classicalspinmodelwithafinitesymmetrygroup
    3.1.3Continuoussymmetrygroup
    3.1.4TheBetheapproximation
    3.1.5Criticalexponents
    3.2Lee-Yangzeroes
    3.2.1TheLee-Yangtheorem
    3.2.2Theone-dimensionalcase
    3.2.3Generalproperties
    3.2.4Zeroesinthetemperatureplane
    3.3Largenlimit
    3.3.1Saddlepointmethod
    3.3.2Factorization
    3.3.3Couplingtoanexternalfield
    3.4Correctionstomeanfield
    3.4.1LaplacetransformNotes

    4ScalingtransformationsandtheXY-model
    4.1Scalinglaws.Realspacerenormalization
    4.1.1Homogeneityandscaleinvariance
    4.1.2Recurrencerelationsinrealspace
    4.1.3Examplesandapproximations
    4.2TheXY-model
    4.2.1Hightemperaturebehaviour
    4.2.2Lowtemperatureexpansion.Vortices
    4.2.3TheVillainaction
    4.2.4Correlations
    4.2.5Renormalizationflow
    4.ATwo-dimensionalsystemswithcontinuoussymmetry
    4.A.1Magnetizationinequality
    4.A.2Correlationinequality
    4.BPhenomenologicalrenormalizationNotes

    5Continuousfieldtheoryandtherenormalizationgroup
    5.1TheLagrangiananddimensionalanalysis
    5.1.1Introduction
    5.1.2Generatingfunctionalsanddimensionalanalysis
    5.2Theperturbativemethod
    5.2.1Diagrammaticseries
    5.2.2Loopexpansion
    5.2.3Evaluationofintegralsanddimensionalcontinuation
    5.2.4Grouptheoreticalfactors
    5.2.5Powercounting
    5.2.6Perturbativcrenormalization
    5.3Therenormalizationgroup
    5.3.1Renormalizationflow
    5.3.2Criticalexponents
    5.3.3FromtheGaussianultravioletfixedpointtotheinfraredcriticalpointindimensionlessthanfour
    5.3.4Correlationfunctionsatthecriticalpoint
    5.3.5Expansionnearthecriticalpoint
    5.3.6Scalinglawsbelowthecriticaltemperature
    5.4Correctionstoscalinglaws
    5.4.1Deviationfromthecriticalpointindimensionlowerthanfour
    5.4.2Logarithmiccorrectionsindimensionfour
    5.4.3Irrelevantoperators
    5.5Numericalresults
    5.5.1e-expansionofcriticalexponents
    5.5.2Equationofstate
    5.5.3Amplituderatios
    5.5.4Three-dimensionalresults
    5.AMulticriticalpointsNotes

    6Latticegaugefields
    6.1Generalities
    6.1.1Presentation
    6.1.2Thecontinuouslimit
    6.1.3OrderparameterandElitzur''stheorem
    6.1.4Duality
    6.2Structureofthephasediagram
    6.2.1Meanfieldapproximation
    6.2.2Correctionstomeanfieldandrestorationofgaugeinvariance
    6.2.3Discretegroups:1/dexpansion
    6.2.4Continuousgroups:computationofcorrections
    6.3Strongcouplingexpansions
    6.3.1Convergence
    6.3.2Characterexpansions
    6.3.3Freeenergy
    6.3.4Stringtensionandrougheningtransition
    6.3.5Massspectrum
    6.4Latticefermions
    6.4.1Thedoublingproblem
    6.4.2TheNielsen-Ninomiyatheorem
    6.4.3Staggeredfermions
    Notes
    Index
  • 内容简介:
    Sometenyearsago,whencompletingwithJ.-B.ZuberaprevioustextonQuantumFieldTheory,theseniorauthorwaspainfullyawarethatlittlementionwasmadethatmethodsinstatisticalphysicsandEuclideanfieldtheorywerecomingcloserandcloser,withcommontoolsbasedontheuseofpathintegralsandtherenormalizationgroupgivinginsightsonglobalstructures.Itwaspartlytofillthisgapthatthepresentbookwasundertaken.Alas,overthefiveyearsthatittooktocometolife,bothsubjectshaveundergoneanewevolution.Disorderedmedia,growthpatterns,complexdynamicalsystemsorspinglassesareamongthenewimportanttopicsinstatisticalmechanics,whilesuperstringtheoryhasturnedtothestudyofextendedsystems,Kaluza-Kleintheoriesinhigherdimensions,anticommutingcoordinates...inanattempttoformulateaunifiedmodelincludingallknowninteractions.Newandsophisticatedtechniqueshaveinvadedstatisticalphysics,rangingfromalgebraicmethodsinintegrablesystemstofractalsetsorrandomsurfaces.Powerfulcomputersorspecialdevicesprovide"experimental"meansforanewbrandoftheoreticalphysicists.Inquantumfieldtheory,applicationsofdifferentialtopology,geometry,Riemannianmanifolds,operatortheory...requireadeeperbackgroundinmathematicsandaknowledgeofsomeofitsmostrecentdevelopments.Asaresult,whensurveyingwhathasbeenincludedinthepresentvolumeinanattempttouncoverthebasicunityofthesesubjects,theauthorshavethesameunsatisfactoryfeelingofnotbeingabletobringthereaderreallyuptodate.Itispresumablythefateofsuchendeavourstoalwayscomeshortofaccomplishingtheirpurpose.
  • 目录:
    ContentsofVolume2
    Preface
    1FromBrownianmotiontoEuclideanfields
    1.1Brownianmotion
    1.1.1Randomwalks
    1.1.2Thesumoverpaths
    1.1.3ThedimensiontwoofBrowniancurves
    1.2Euclideanfields
    1.2.1Freefields
    1.2.2Interactingfieldsandrandomwalks
    1.2.3Self-avoidingwalksandthelimitn→0
    1.2.4Comparisonwiththehightemperatureexpansion
    1.2.5Theone-dimensionalcase
    1.ALattices
    Notes

    2Grassmannianintegralsandthetwo-dimensionalIsingmodel
    2.1Grassmannianintegrals
    2.1.1Anticommutingvariables
    2.1.2Integrals
    2.2Thetwo-dimensionalIsingmodel
    2.2.1Duality
    2.2.2Transfermatrix
    2.2.3Fermionicrepresentation
    2.2.4Freeenergy
    2.2.5Spontaneousmagnetization
    2.2.6Correlationfunctioninthehightemperaturephase
    2.2.7Surfacetension
    2.3Criticalcontinuoustheory
    2.3.1Effectiveaction
    2.3.2Correlationfunctions
    2.AQuadraticdifferencesandPainleveequationsNotes

    3Spontaneoussymmetrybreaking,meanfield
    3.1Meanfieldapproximation
    3.1.1Dielectriccoastantofapolarizablemedium
    3.1.2Classicalspinmodelwithafinitesymmetrygroup
    3.1.3Continuoussymmetrygroup
    3.1.4TheBetheapproximation
    3.1.5Criticalexponents
    3.2Lee-Yangzeroes
    3.2.1TheLee-Yangtheorem
    3.2.2Theone-dimensionalcase
    3.2.3Generalproperties
    3.2.4Zeroesinthetemperatureplane
    3.3Largenlimit
    3.3.1Saddlepointmethod
    3.3.2Factorization
    3.3.3Couplingtoanexternalfield
    3.4Correctionstomeanfield
    3.4.1LaplacetransformNotes

    4ScalingtransformationsandtheXY-model
    4.1Scalinglaws.Realspacerenormalization
    4.1.1Homogeneityandscaleinvariance
    4.1.2Recurrencerelationsinrealspace
    4.1.3Examplesandapproximations
    4.2TheXY-model
    4.2.1Hightemperaturebehaviour
    4.2.2Lowtemperatureexpansion.Vortices
    4.2.3TheVillainaction
    4.2.4Correlations
    4.2.5Renormalizationflow
    4.ATwo-dimensionalsystemswithcontinuoussymmetry
    4.A.1Magnetizationinequality
    4.A.2Correlationinequality
    4.BPhenomenologicalrenormalizationNotes

    5Continuousfieldtheoryandtherenormalizationgroup
    5.1TheLagrangiananddimensionalanalysis
    5.1.1Introduction
    5.1.2Generatingfunctionalsanddimensionalanalysis
    5.2Theperturbativemethod
    5.2.1Diagrammaticseries
    5.2.2Loopexpansion
    5.2.3Evaluationofintegralsanddimensionalcontinuation
    5.2.4Grouptheoreticalfactors
    5.2.5Powercounting
    5.2.6Perturbativcrenormalization
    5.3Therenormalizationgroup
    5.3.1Renormalizationflow
    5.3.2Criticalexponents
    5.3.3FromtheGaussianultravioletfixedpointtotheinfraredcriticalpointindimensionlessthanfour
    5.3.4Correlationfunctionsatthecriticalpoint
    5.3.5Expansionnearthecriticalpoint
    5.3.6Scalinglawsbelowthecriticaltemperature
    5.4Correctionstoscalinglaws
    5.4.1Deviationfromthecriticalpointindimensionlowerthanfour
    5.4.2Logarithmiccorrectionsindimensionfour
    5.4.3Irrelevantoperators
    5.5Numericalresults
    5.5.1e-expansionofcriticalexponents
    5.5.2Equationofstate
    5.5.3Amplituderatios
    5.5.4Three-dimensionalresults
    5.AMulticriticalpointsNotes

    6Latticegaugefields
    6.1Generalities
    6.1.1Presentation
    6.1.2Thecontinuouslimit
    6.1.3OrderparameterandElitzur''stheorem
    6.1.4Duality
    6.2Structureofthephasediagram
    6.2.1Meanfieldapproximation
    6.2.2Correctionstomeanfieldandrestorationofgaugeinvariance
    6.2.3Discretegroups:1/dexpansion
    6.2.4Continuousgroups:computationofcorrections
    6.3Strongcouplingexpansions
    6.3.1Convergence
    6.3.2Characterexpansions
    6.3.3Freeenergy
    6.3.4Stringtensionandrougheningtransition
    6.3.5Massspectrum
    6.4Latticefermions
    6.4.1Thedoublingproblem
    6.4.2TheNielsen-Ninomiyatheorem
    6.4.3Staggeredfermions
    Notes
    Index
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