stringnotes-'t hooft

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1、INTRODUCTIONTOSTRINGTHEORY¤version14-05-04Gerard’tHooftInstituteforTheoreticalPhysicsUtrechtUniversity,Leuvenlaan43584CCUtrecht,theNetherlandsandSpinozaInstitutePostbox80.1953508TDUtrecht,theNetherlandse-mail:g.thooft@phys.uu.nlinternet:http://www.phys.uu.nl/~thooft/Contents1StringsinQCD.41

2、.1Thelineartrajectories..............................41.2TheVenezianoformula..............................52Theclassicalstring.73Openandclosedstrings.113.1TheOpenstring.................................113.2Theclosedstring.................................123.3Solutions.......................

3、..............123.3.1Theopenstring.............................123.3.2Theclosedstring.............................133.4Thelight-conegauge...............................143.5Constraints....................................153.5.1foropenstrings:.............................16¤Lecturenotes2003a

4、nd200413.5.2forclosedstrings:............................163.6Energy,momentum,angularmomentum....................174Quantization.184.1Commutationrules................................184.2Theconstraintsinthequantumtheory.....................194.3TheVirasoroAlgebra............................

5、..204.4Quantizationoftheclosedstring.......................234.5Theclosedstringspectrum...........................245Lorentzinvariance.256Interactionsandvertexoperators.277BRSTquantization.318ThePolyakovpathintegral.Interactionswithclosedstrings.348.1Theenergy-momentumtensorfortheghostfields

6、...............369T-Duality.389.1Compactifyingclosedstringtheoryonacircle.................399.2T-dualityofclosedstrings............................409.3T-dualityforopenstrings............................419.4Multiplebranes..................................429.5Phasefactorsandnon-coincidingD

7、-branes..................4210Complexcoordinates.4311Fermionsinstrings.4511.1Spinningpointparticles.............................4511.2ThefermionicLagrangian............................4611.3Boundaryconditions...............................4911.4Anticommut