intro to string theory - g. terhooft

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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/~

2、thooft/Contents1StringsinQCD.41.1Thelineartrajectories..............................41.2TheVenezianoformula..............................52Theclassicalstring.73Openandclosedstrings.113.1TheOpenstring.................................113.2Theclosedstring........

3、.........................123.3Solutions.....................................123.3.1Theopenstring.............................123.3.2Theclosedstring.............................133.4Thelight-conegauge...............................143.5Constraints..............

4、......................153.5.1foropenstrings:.............................16¤Lecturenotes2003and200413.5.2forclosedstrings:............................163.6Energy,momentum,angularmomentum....................174Quantization.184.1Commutationrules.................

5、...............184.2Theconstraintsinthequantumtheory.....................194.3TheVirasoroAlgebra..............................204.4Quantizationoftheclosedstring.......................234.5Theclosedstringspectrum...........................245Lorentzinvariance.2

6、56Interactionsandvertexoperators.277BRSTquantization.318ThePolyakovpathintegral.Interactionswithclosedstrings.348.1Theenergy-momentumtensorfortheghostfields...............369T-Duality.389.1Compactifyingclosedstringtheoryonacircle.................399.2T-dualityo

7、fclosedstrings............................409.3T-dualityforopenstrings............................419.4Multiplebranes..................................429.5Phasefactorsandnon-coincidingD-branes..................4210Complexcoordinates.4311Fermionsinstrings.4511

8、.1Spinningpointparticles.............................4511.2ThefermionicLagrangian............................4611.3Boundaryconditions...............................4911.4Anticommut