資源描述：
《lectures on topological quantum field theory》由會員上傳分享，免費在線閱讀，更多相關內容在學術論文-天天文庫。
1、CERN-TH/97-250US-FT-30/97hep-th/9709192September1997LecturesonTopologicalQuantumFieldTheory1J.M.F.Labastidaa;bandCarlosLozanobaTheoryDivision,CERN,CH-1211Geneva23,Switzerland.bDepartamentodeFsicadePartculas,UniversidadedeSantiagodeCompostela,E-15706SantiagodeCompostela,Spain.Abstr
2、actIntheselectureswepresentageneralintroductiontotopologicalquantum eldtheories.ThesetheoriesarediscussedintheframeworkoftheMathai-Quillenfor-malismandinthecontextoftwistedN=2supersymmetrictheories.WediscussarXiv:hep-th/9709192v126Sep1997indetailtherecentdevelopmentsinDonaldson-Witten
3、theoryobtainedfromtheap-plicationofresultsbasedondualityforN=2supersymmetricYang-Millstheories.ThisinvolvesadescriptionofthecomputationofDonaldsoninvariantsintermsofSeiberg-Witteninvariants.GeneralizationsofDonaldson-Wittentheoryarereviewed,andthestructureofthevacuumexpectationvalueso
4、ftheirobservablesisanalyzedinthecontextofdualityforthesimplestcase.1LecturesgivenattheworkshopTrendsinTheoreticalPhysics",CERN-SantiagodeCompostela-LaPlataMeeting,heldinLaPlata,Argentina,April28-May61997.Contents1Introduction12TopologicalQuantumFieldTheory53TheMathai-Quillenformalism
5、123.1Finite-dimensionalcase..........................133.2In nite-dimensionalcase.........................203.2.1Supersymmetricquantummechanics..............213.2.2Topologicalsigmamodels....................254Donaldson-WittenTheory284.1TwistofN=2supersymmetry.....................304.2
6、Perturbativeapproach..........................334.3Non-perturbativeapproach........................344.3.1Donaldsoninvariants:abstractapproach............354.3.2Donaldsoninvariants:concreteapproach............385GeneralizedDonaldson-WittenTheory506Finalremarks561IntroductionTopologica
7、lquantum eldtheory(TQFT)emergedintheeightiesasanewrelationbetweenmathematicsandphysics.Thisrelationconnectedsomeofthemostadvancedideasinthetwo elds.Theninetieshavebeencharacterizedbyitsdevelopment,originatingunexpectedresultsintopologyandtestingsomeofthemostfundamentalideasinquantum e
8、ldthe
