An Introduction to Quantum Field Theory (Mrinal Dasgupta)

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1、AnIntroductiontoQuantumFieldTheoryMrinalDasguptaSchoolofPhysicsandAstronomyUniversityofManchesterManchesterOxfordRoad,M139PL,UK.LecturespresentedattheRALSchoolforHighEnergyPhysicists,SomervilleCollege,Oxford,September2008.Contents0Prologue1Introduction1.1Lagrangi

2、anformalisminclassicalmechanics1.2Quantummechanics1.3TheSchr¨odingerpicture1.4TheHeisenbergpicture1.5ThequantummechanicalharmonicoscillatorProblems2ClassicalFieldTheory2.1FromN-pointmechanicstofieldtheory2.2Relativisticfieldtheory2.3Actionforascalarfield2.4Planewave

3、solutiontotheKlein-Gordonequation2.5.SymmetriesandconservationlawsProblemsQuantumFieldTheory3.1Canonicalfieldquantisation3.2Causalityandcommutationrelations3.3Creationandannihilationoperators3.4Energyofthevacuumstateandrenormalisation3.5Fockspaceandparticlenumberr

4、epresentationProblems4Interactingscalarfields4.1TheS-matrix4.2Moreontimeevolution:Diracpicture4.3S-matrixandGreen’sfunction4.4HowtocomputeGreen’sfunctionsProblems5PerturbationTheory5.1Wick’sTheorem5.2TheFeynmanpropagator5.3Two-particlescatteringtoO(λ)5.4Graphicalr

5、epresentationoftheWickexpansion:Feynmanrules5.5Feynmanrulesinmomentumspace5.6S-matrixandtruncatedGreen’sfunctionsProblems6ConcludingremarksAcknowledgementsANotationandconventionsWhenIbecameastudentofPomeranchukin1950IheardfromhimakindofjokethattheBookofPhysicshad

6、twovolumes:vol.1isPumpsandManometers,vol.2isQuantumFieldTheoryLevOkun0PrologueThedevelopmentofQuantumFieldTheoryissurelyoneofthemostimportantachieve-mentsinmodernphysics.Presently,allobservationalevidencepointstothefactthatQuantumFieldTheory(QFT)providesagooddesc

7、riptionofallknownelementaryparti-cles,aswellasforparticlephysicsbeyondtheStandardModelforenergiesranginguptothePlanckscale∼1019GeV,wherequantumgravityisexpectedtosetinandpresumablyrequiresanewanddifferentdescription.Historically,QuantumElectrodynamics(QED)emergeda

8、stheprototypeofmodernQFT’s.Itwasdevelopedinthelate1940sandearly1950schieflybyFeynman,SchwingerandTomonaga,andisperhapsthemostsuccessfultheoryinphysics:theanomal