introduction to relativistic quantum field theory - h. vanhees

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1、IntroductiontoRelativisticQuantumFieldTheoryHendrikvanHees1Fakult¨atf¨urPhysikUniversit¨atBielefeldUniversit¨atsstr.25D-33615Bielefeld25thJune20031e-mail:hees@physik.uni-bielefeld.de2Contents1PathIntegrals111.1QuantumMechanics................................111.2ChoiceofthePicture.........

2、.......................131.3FormalSolutionoftheEquationsofMotion...................161.4Example:TheFreeParticle............................181.5TheFeynman-KacFormula............................201.6ThePathIntegralfortheHarmonicOscillator..................231.7SomeRulesforPathIntegrals.....

3、......................251.8TheSchr¨odingerWaveEquation.........................261.9PotentialScattering................................281.10GeneratingfunctionalforVacuumExpectationValues.............341.11BosonsandFermions,andwhatelse?.......................352NonrelativisticMany-Particle

4、Theory372.1TheFockSpaceRepresentationofQuantumMechanics............373CanonicalFieldQuantisation413.1SpaceandTimeinSpecialRelativity.......................423.2TensorsandScalarFields.............................463.3Noether’sTheorem(ClassicalPart)........................513.4CanonicalQuant

5、isation..............................553.5TheMostSimpleInteractingFieldTheory:φ4.................603.6TheLSZReductionFormula...........................623.7TheDyson-WickSeries..............................643.8Wick’sTheorem..................................663.9TheFeynmanDiagrams..........

6、....................684RelativisticQuantumFields754.1CausalMassiveFields...............................764.1.1MassiveVectorFields...........................773Contents4.1.2MassiveSpin-1/2Fields..........................784.2CausalMasslessFields...............................824.2.1Massless

7、VectorField...........................824.2.2MasslessHelicity1/2Fields........................844.3QuantisationandtheSpin-StatisticsTheorem..................854.3.1Quantisationofthespin-1/2DiracField.................854.4DiscreteSymmetriesandtheCPTTheorem.....