Mathematical Aspects of Quantum Field Theory

《Mathematical Aspects of Quantum Field Theory》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、MathematicalAspectsofQuantumFieldTheoryEdsondeFariaandWelingtondeMeloContentsForewordpage8Preface101ClassicalMechanics131.1NewtonianMechanics131.1.1Newtonianspacetime131.1.2Newtonianconfigurationspace141.2LagrangianMechanics161.2.1Lagrangiansystems161.

2、2.2Theleastactionprinciple161.2.3TheEulerLagrangeequations171.2.4ConservativeLagrangiansystems181.3HamiltonianMechanics191.3.1TheLegendretransformation191.3.2Symplecticmanifolds201.3.3Hamiltoniansystems211.3.4Hamiltonianofaconservativesystem231.4Poiss

3、onbrackets231.5Symmetryandconservationlaws:Noether’sTheorem242Quantummechanics272.1Thebirthofquantumtheory272.2Thebasicprinciplesofquantummechanics292.2.1Statesandobservables292.2.2Timeevolution312.2.3Symmetries322.2.4Heisenberg’suncertaintyprinciple3

4、22.2.5ThevonNeumannaxioms332.3Canonicalquantization3434Contents2.4TheC∗algebraapproach372.5TheWeylC∗algebra392.6Thequantumharmonicoscillator432.6.1Computingthespectrum432.6.2Concretecoordinaterepresentation472.6.3Holomorphicrepresentation482.7Angularm

5、omentumquantizationandspin492.8Pathintegralquantization532.8.1TheTrotterproductformula542.8.2Theheuristicpathintegral572.9Deformationquantization633Relativity,theLorentzgroupandDirac’sequation653.1RelativityandtheLorentzgroup653.1.1Postulates653.1.2Lo

6、rentztransformations673.2Relativistickinematics703.3Relativisticdynamics713.4TherelativisticLagrangian723.5Dirac’sequation744FiberBundles,ConnectionsandRepresentations804.1Fiberbundlesandcocycles804.2Principalbundles844.3Connections874.4Thegaugegroup8

7、94.5TheHodge⋆operator904.6Cliffordalgebrasandspinorbundles924.6.1Cliffordalgebras924.6.2RepresentationsofSpin(V)andtheDiracoperator944.6.3Spinbundlesoveraspacetimemanifold954.6.4Abstractactions964.7Representations984.7.1TheLorentzandPoincar´egroups984.7

8、.2Inducedrepresentationsofunitarytype1004.7.3Wigner’sclassificationofparticles1034.7.4SpinorrepresentationsofSL(2,C)1075ClassicalFieldTheory1105.1Introduction1105.2ElectromagneticField1115.2.1Maxwell’sequations111Contents55.2.2Thescalarandvecto