**Fields v4**contains the lecture notes for the class.*Warning*: This book and web page are being revised*during*the course.- It may help to have a copy of the relevant subsections available during class (preferably in digital form) for annotation, or help in asking questions (especially prepared ones).

**Assigned reading**is crucial for you to prepare questions ahead of class.- It includes @ least 2 subsections ahead of lecture (including the homework problems to be assigned).
- Skim the background material to see if you need it.
- Also note the summaries given in the
**Outline**@ the beginning of the book, & for equations the**AfterMath**@ the end. - If you miss or are late to class, you are responsible for any material you missed: See me in private or ask fellow students.

**Homework**is essential to help you understand the lecture, & as preparation for the exams.- It's due 1 week after reached in lecture, @ beginning of class, & returned @ the beginning of the following class.
- You can submit it on paper in class, or electronically; if on paper, don't turn in different assignments on the same sheet or you won't get it back till the latest is returned.
- Late homework is not accepted.
**There will be some discussion of the homework in class**, @ the beginning of the lecture when it's returned. More hints will be given for problems students had difficulties with, but not all the algebra will be worked out. You are encouraged to give a second try on problems you failed to complete, for your own edification (not for turning in).

S(cattering)-matrices | in subsections | background material & homework |
---|---|---|

in quantum mechanics | ||

- time development
- causality, unitarity
- path integrals
| VA1 | |

- S-matrix
- causality, unitarity
| VA4 | VA4.2 (due 4/19) |

in relativistic quantum mechanics | IIIB3-5 (external fields), VA3 (iε ℞) | |

- 1st-quantization → propagator
- covariant gauge
- lightcone gauge
| VB1 | VB1.1 (due 4/22) |

- vertex operators
- 1st-quantized S-matrix
| VIIIC5 (1st ⅓) | |

Regge theory | ||

Γ functions | ||

- Schwinger/Feynman parameters
- Γ & B functions
| VIIA2 | VIIA2.2-3 (due 4/22) |

(J)WKB (semiclassical expansion) | IB3 (determinants), VA5 (Wick rotation) | |

- classical
- "1-loop"
| VA2 | IIIA4.2 (due 4/22), VA2.1, VIIC2.2 (due 4/24) |

in quantum mechanics | IA4 (Mandelstam variables) | |

- Coulomb scattering
- eikonal approximation
- bound-state poles
| VIIA6 (2nd ½) | VIIA6.2 (due 4/24) |

in relativistic quantum mechanics | ||

- ladders: s & t channels
- complex angular momentum
- spectrum vs. high energy
- s-t duality
| XIA1 | XIA1.2-3 (due 4/26) |

strings | ||

open strings | VC9 (groups), XIB1-5 (l.c.,spectrum,weights) | |

- tachyon vertex
- amplitudes
- Regge behavior, duality
- fixed angle
| XIB6 | XIB6.1-3 (due 4/29) |

closed strings | ||

- open-string factorization
- amplitude
| XIB7 | XIB7.1-2 (due 5/1) |

nonperturbative | VIIC4 (1/N expansion) | |

- random lattice
- partons
| XIA7 (1st ½) | VB1.2, XIA7.1 (due 5/3) |

ghosts | ||

measure | ||

- vacua
- Sp(2)
| XIB8 | XIB8.2-3 (due 5/6) |

vertex operators | ||

- BRST
- massless vector
| XIB9 | XIB9.1 (due 5/8) |

Green-Schwarz superstrings | ||

triality | VIIB5 (bosonization) | |

- vertex operators
- spinors
- RNS ↔ GS
| XIB5 | |

superparticle | IIC (supersymmetry), IIIB1 (scalar particle) | |

- Hamiltonian
- constraints
- lightcone gauge
| IIIB6 | |

superstring | IC6, IVA3 (cosets), XC5 (Fierz), XIA5 (T-duality) | |

- currents
- action
- lightcone gauge
| XIA9 | |

loops | ||

topology | VIIC4 (1/N expansion), XIA7 (Euler number) | |

- 1-loop insertions
- lower loops
- divergence cancelation
| XIA2 | |

string types | IA5 (worldline symmetry) | |

- worldsheet symmetries
- groups
- orientability
- supersymmetries
| XIA4 |