quantum field theory at finite temperature an introduction

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1、T00/055QUANTUMFIELDTHEORYATFINITETEMPERATURE:ANINTRODUCTIONJ.ZINN-JUSTIN*CEA-Saclay,ServicedePhysiqueTheorique**,F-91191Gif-sur-YvetteCedex,FRANCE.andUniversityofCergy-PontoiseABSTRACTInthesenoteswereviewsomepropertiesofStatisticalQuantumFieldTheoryatequilibrium,i.eQu

2、antumFieldTheoryatnitetemperature.Weexplaintherelationbetweennitetemperaturequantumeldtheoryin(d;1)dimensionsandstatisticalclassicaleldtheoryind+1dimensions.ThisidenticationallowstoanalyzethenitetemperatureQFTintermsoftherenormalizationgroupandthetheoryofnitesiz

3、eeectsoftheclassicaltheory.Wediscussinparticularthelimitofhightemperature(HT)orthesituationofnitetemperaturephasetransitions.Theretheconceptofdimensionalreductionplaysanessentialrole.Dimensionalreductioninsomesensere ectstheknownpropertythatquantumarXiv:hep-ph/000527

4、2v126May2000eectsarenotimportantathightemperature.4Weillustratetheseideaswithseveralstandardexamples,eldtheory,thenon-linearmodelandtheGross{Neveumodel,gaugetheories.Weconstructthecorrespondingeectivereducedtheoriesatone-looporder,usingthetechniqueofmodeexpansiono

5、feldsintheimaginarytimevariable.InmodelswheretheeldisavectorwithNcomponents,thelargeNexpansionprovidesanotherspeciallyconvenienttooltostudydimensionalreduction.email:zinn@spht.saclay.cea.frLaboratoiredelaDirectiondesSciencesdelaMatiereduCommissariatal'EnergieAto

6、mique2Contents1Finite(andhigh)temperatureeldtheory:Generalremarks......21.1Finitetemperaturequantumeldtheory.............21.2Dimensionalreductionandeectiveeldtheory..........42Theexampleofthe4quantumeldtheory............6d;12.1Renormalizationgroupatnitetemperatu

7、re............72.2One-loopeectiveaction....................93Hightemperatureandcriticallimits...............123.1Dimensiond=4.......................133.2Dimensiond3.......................154Thenon-linearmodelinthelargeNlimit............184.1ThelargeNlimitatzerotempe

8、rature.............184.2Finitetemperature......................205Thenon-linearmodel:Dimensionalreduction..........2