finite temperature field theory and phase transition

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1、FiniteTemperatureFieldTheoryandPhaseTransitionsM.-P.LombardoIstitutoNazionalediFisicaNucleare,SezionediPadovaeGruppoCollegatodiTrento,ItalyarXiv:hep-ph/0103141v224May2001Lecturesgivenatthe:SummerSchoolonAstroparticlePhysicsandCosmologyTrieste,12{30June2000LNS

2、lombardo@science.unitn.itAbstractTheselecturesreviewphasesandphasetransitionsoftheStandardModel,withemphasisonthoseaspectswhichareamenabletoarstprinciplestudy.Modelcalcu-lationsandtheoreticalideasofpracticalapplicabilityarediscussedaswell.Contents:1.Overview

3、;2.FieldTheoryatFiniteTemperatureandDensity;3.CriticalPhenom-ena;4.ElectroweakInteractionsatFiniteTemperature;5.ThermodynamicsofFourFermionsmodels;6.ThePhasesofQCD;7.QCDatFiniteTemperature,B=0;8.QCDatFiniteTemperature,B6=0.Contents1Overview12EquilibriumField

4、TheoryatFiniteTemperature22.1FunctionalIntegralRepresentationofZ....................22.2TheIdeaofDimensionalReduction.......................42.3ModeExpansionandDecoupling........................52.4FiniteTemperature{Summary..........................53CriticalP

5、henomena63.1TheEquationofStateandtheCriticalExponents...............63.2TheEectivePotential..............................83.3ACaseStudy...................................93.4DynamicalSymmetryBreaking.........................104ElectroweakInteractionsatFiniteT

6、emperature114.1PerturbativeAnalysis...............................114.2FourDimensionalLatticeStudy.........................134.3ThreeDimensionalEectiveAnalysis......................144.4ThePhaseDiagramoftheEWSectoroftheStandardModel.........145Thermodynamicso

7、fFourFermionsModels156ThePhasesofQCD197QCDatFiniteTemperature,B=0207.1QCDHighTP.T.,andSymmetriesI:mq=0andtheChiralTransition..227.2TwoColorQCDI.................................237.3QCDHighTp.t.,andSymmetriesII:mq=1andtheConnementTransition237.4TwoColorQCDII.

8、...............................247.5SummaryandOpenQuestionsfortheQCDHighTTransition........258QCDatFiniteTemperature,B6=0268.1TheLatticeStrongCouplingAnalysisoftheQCDPhaseDiagram.