IntroducedasaquantumextensionofMaxwell’sclassicaltheory,quantumelectrodynamicshasbeenthefirstexampleofaQuantumFieldTheory(QFT).Eventually,QFThasbecometheframeworkforthediscussionofallfundamentalinteractionsatthemicroscopicscaleexcept,possibly,gravity.Moresurprisingly,ithasalsoprovidedaframeworkfortheunderstandingofsecondorderphasetransitionsinstatisticalmechanics.Asthisworkillustrates,QFTisthenaturalframeworkforthediscussionofmostsystemsinvolvinganinfinitenumberofdegreesoffreedomwithlocalcouplings.ThesesystemsrangefromcoldBosegasesatthecondensationtemperature(abouttennanokelvin)toconventionalphasetransitions(fromafewdegreestoseveralhundred)andhighenergyparticlephysicsuptoaTeV,altogethermorethantwentyordersofmagnitudeintheenergyscale.Therefore,thistextsetsouttopresentaworkinwhichthestrongformalrelationsbetweenparticlephysicsandthetheoryofcriticalphenomenaaresystematicallyemphasized.Thisoptionexplainssomeofthechoicesmadeinthepresentation.AformulationintermsoffieldintegralshasbeenadoptedtostudythepropertiesofQFT.Thelanguageofpartitionandcorrelationfunctionshasbeenusedthroughout,eveninapplicationsofQFTtoparticlephysics.Renormalizationandrenormalizationgrouppropertiesaresystematicallydiscussed.Thenotionofeffectivefieldtheoryandtheemergenceofrenormalisabletheoriesaredescribed.Theconsequencesforfinetuningandtrivialityissueareemphasized.Thisfiftheditionhasbeenupdatedandfullyrevised,e.g.inparticlephysicswithprogressinneutrinophysicsandthediscoveryoftheHiggsboson.Thepresentationhasbeenmademorehomogeneousthrougoutthevolume,andemphasishasbeenputonthenotionofeffectivefieldtheoryanddiscussionoftheemergenceofrenormalisabletheories.
GRAVITY FIELD QUANTUM THEORY THEREFORE
