- ⚠️ Any material may be revised
*during*the course. **Fields v4**contains the lecture notes for the class.- Skim the
**background material**to see if you need it. (Some of it is unnecessary, but perhaps interesting elaboration.) - Brief summaries of each subsection are given in the
**Outline**@ the beginning of the book. - Major equations (especially notation & definitions) are collected in the
**AfterMath**@ the end.

- Skim the
**Assigned reading**is crucial.- It includes @ least 2 subsections ahead of lecture, including the
**homework problems**to be assigned. - Have a copy of the relevant parts available during class (preferably in digital form) for following, annotation, & flipping back to earlier relevant pages.
- If you miss or are late to class, you are responsible for any material you missed: See me in private or ask fellow students.

- It includes @ least 2 subsections ahead of lecture, including the
**Prepare questions**in advance for class.- Find points that were unclear to you in the assigned reading (including background material & homework). The book
*Fields*is my lecture notes, so just listening to me lecture without questions, as a repeat of what you've already read, probably won't be helpful. Lectures aren't YouTube videos. - Prepared annotation of this book & supplementary notes is useful for asking questions @ the appropriate points, in case confusion hasn't already been cleared up by then.

- Find points that were unclear to you in the assigned reading (including background material & homework). The book
**Homework**is essential.- It tests whether you understand the lecture.
- If you can't do the homework, you probably won't do well on the exams.
- It's due 1 week after reached in lecture, by the beginning of class.
- 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).

- strong interactions @ small angles (original motivation)
- finite quantum gravity

topology | in subsections | background material & homework |
---|---|---|

graph topology | ||

- P−V = L−1
| VC2 (last ⅕) | |

1/N_{color} expansion | ||

- color loops
- Euler number
- flavor
| VIIC4 | |

worldsheet topology | ||

- duality
- tadpoles
- open→closed
| XIA2 | XIA2.1 (due 3/19) |

particle propagators | IIIA1 (Dirac δ), IIIB (classical), VA3 (nonrelativistic) | |

- proper time
- iε ℞
- energy sign
| VB1 | VB1.1 (due 3/19) |

1st-quantized particle graphs | ||

- Schwinger parameters
- 1st-q action
| VC8 | |

worldsheet lattices | VA5,VB4 (Wick rotation) | |

- discrete worldsheet
- string action
- preon propagators
| XIA7 (1st ½) | XIA7.1 (due 3/22) |

particle scattering | ||

1st-q S-matrices | IIIB3 (background fields), VA4 (nonrelativistic) | |

- perturbation
- interaction picture
- Green function
- loops
| VIIIC5 | VA4.2 (due 3/22) |

Γ functions | ||

- Schwinger parametrization
- Beta function
| VIIA2 | VIIA2.2,3, VIIC2.2 (due 3/26) |

Coulomb scattering | IA4 (Mandelstam variables), VA2 (JWKB) | |

- eikonal approximation
- strong coupling
- infrared
| VIIA6 (2nd ½) | VIIA6.2 (due 3/26) |

string trees | ||

Regge behavior | ||

- ladders
- complex angular momentum
- duality
| XIA1 | XIA1.2 (due 3/29) |

open trees | ||

- 4 tachyons
- limits
- higher-point
| XIB6 | XIB6.2 (due 3/31) |

closed trees | ||

- Schwinger parameters
- 4 tachyons
- open factorization
| XIB7 | XIB7.1,2 (due 4/5) |

ghosts | ||

measure | ||

- vacua
- Sp(2)
| XIB8 | XIB8.2,3 (due 4/5) |

vertex operators | ||

- BRST
- massless vector
| XIB9 | XIB9.1 (due 4/7) |

string loops | (as time permits) | |

partition function | ||

- integration measure
- ghosts
| XIC1 | |

Jacobi Θ functions | VIIB5 (bosonization) | |

- bosonization
- symmetries
- phase transition
| XIC2 | XIC2.1 (due 4/9) |

Green function | ||

- periodicity
- SL(2,Z)
| XIC3 | XIC3.1 (due 4/12) |

open | ||

- poles
- annulus
- Möbius strip
- group theory
| XIC4 | XIC4.1 (due 4/14) |

closed | ||

- SL(2,Z)
- fundamental domain
- divergences
| XIC5 |