| Topology | in subsections | background material & homework | 
|---|
| graph topology |  | 
|  | VC2 (last ⅕) |  | 
| group theory via graphs | IB1 (matrices), IC4 (color & flavor) | 
| index linesFeynman graphs
 | VC9 | VC9.1 (due 10/28) | 
| 1/Ncolor expansion |  | 
| color loopsEuler numberflavor
 | VIIC4 |  | 
| worldsheet topology |  | 
| dualitytadpolesopen→closed
 | XIA2 | XIA2.1 (due 11/1) | 
| discrete worldline symmetries | IA4 (proper time) | 
|  | IA5 |  | 
| string theory typology | IB4-5 (SO/Sp groups) | 
| Chan-Patonworldsheet CPTorientationsupersymmetry
 | XIA4 | XIA4.1 (due 11/4) | 
| Geometry |  | 
|---|
| particle propagators | IIIA1 (Dirac δ), IIIB (classical), VA3 (nonrelativistic) | 
| proper timeiε ℞energy sign
 | VB1 | VB1.1 (due 11/6) | 
| 1st-quantized particle graphs |  | 
| Schwinger parameters1st-q action
 | VC8 |  | 
| worldsheet lattices | VA5,VB4 (Wick rotation) | 
| discrete worldsheetstring actionpreon propagators
 | XIA7 (1st ½) | XIA7.1 (due 11/6) | 
| Particle scattering |  | 
|---|
| 1st-q S-matrices | IIIB3 (background fields), VA4 (nonrelativistic) | 
| perturbationinteraction pictureGreen functionloops
 | VIIIC5 |  | 
| Γ functions |  | 
| Schwinger parametrizationBeta function
 | VIIA2 | VIIA2.2,3, VIIC2.2 (due 11/11) | 
| Coulomb scattering | IA4 (Mandelstam variables), VA2 (JWKB) | 
| eikonal approximationstrong couplinginfrared
 | VIIA6 (2nd ½) | VIIA6.2 (due 11/13) | 
| String trees |  | 
|---|
| Regge behavior |  | 
| ladderscomplex angular momentumduality
 | XIA1 | XIA1.2 (due 11/15) | 
| Green functions |  | 
| cylinder→planeclosed→open
 | XIB2 (last ⅖) | VIIB1.1 (due 11/15) | 
| Open trees |  | 
| 4 tachyonslimitshigher-point
 | XIB6 | XIB6.2 (due 11/18) | 
| Closed trees |  | 
| Schwinger parameters4 tachyonsopen factorization
 | XIB7 | XIB7.1,2 (due 11/22) | 
| Green-Schwarz |  | 
|---|
| supersymmetry |  | 
| algebrapositivitymassless
 | IIC1 |  | 
| superspace |  | 
| coordinatescovariant derivatives
 | IIC2 |  | 
| superparticle | IIIB1-2 (scalar particle) | 
| Hamiltonianconstraintslightcone gauge
 | IIIB6 | IIIB6.1 (due 11/25) | 
| superstring | XIA5 (T-duality) | 
| currentsactionlightcone gauge
 | XIA9 |  |