非交换几何、量子场论与动机(主题)（孔涅）

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1、NoncommutativeGeometry,QuantumFieldsandMotivesAlainConnesMatildeMarcolliA.Connes:CollegedeFrance,3,rued'Ulm,Paris,F-75005France,µI.H.E.S.andVanderbiltUniversityE-mailaddress:alain@connes.orgM.Marcolli:Max{PlanckInstitutfurMathematik,Vivatsgasse7,ÄBonn,D-53111German

2、yE-mailaddress:marcolli@mpim-bonn.mpg.deContentsPreface9Chapter1.Quantum¯elds,noncommutativespaces,andmotives171.Introduction172.BasicsofperturbativeQFT222.1.LagrangianandHamiltonianformalisms232.2.LagrangianandtheFeynmanintegral252.3.TheHamiltonianandcanonicalquan

3、tization262.4.Thesimplestexample282.5.Green'sfunctions312.6.WickrotationandEuclideanGreen'sfunctions323.Feynmandiagrams353.1.Thesimplestcase363.2.Theoriginsofrenormalization403.3.Feynmangraphsandrules433.4.ConnectedGreen'sfunctions473.5.Thee®ectiveactionandone-part

4、icleirreduciblegraphs483.6.Physicallyobservableparameters523.7.Thephysicsideaofrenormalization544.Dimensionalregularization565.ThegraphbygraphmethodofBogoliubov{Parasiuk{Hepp{Zimmermann625.1.Thesimplestexampleofsubdivergence635.2.Super¯cialdegreeofdivergence675.3.S

5、ubdivergencesandpreparation686.TheConnes{Kreimertheoryofperturbativerenormalization746.1.CommutativeHopfalgebrasanda±negroupschemes756.2.TheHopfalgebraofFeynmangraphs:discretepart786.3.TheHopfalgebraofFeynmangraphs:fullstructure856.4.BPHZasaBirkho®factorization886.

6、5.Di®eographismsanddi®eomorphisms936.6.Therenormalizationgroup957.RenormalizationandtheRiemann{Hilbertcorrespondence1007.1.Countertermsandtime-orderedexponentials1017.2.Flatequisingularconnections1077.3.EquivariantprincipalbundlesandthegroupG¤=GoGm1167.4.Tannakianc

7、ategoriesanda±negroupschemes1217.5.Di®erentialGaloistheoryandthelocalRiemann{Hilbertcorrespondence1247.6.UniversalHopfalgebraandtheRiemann{Hilbertcorrespondence1283CONTENTS48.Motivesinanutshell1368.1.Algebraicvarietiesandmotives1368.2.Puremotives1448.3.Mixedmotives

8、1488.4.MixedHodgestructures1528.5.Tatemotives,periods,andquantum¯elds1559.TheStandardModelofelementaryparticles1569.1.Particlesandinteractions158