Siegel's lectures, PHY 623, S'21

⚠️ 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.
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.
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.
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).

What are strings good for?

High-energy scattering: They're the only workable (although flawed) models of

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

Calculations use perturbation theory, which produces much more calculable results than nonperturbative methods (@ least in > 2 dimensions), & for high energy (cross sections), not just low (masses, couplings, effective potentials). (An intermediate case is perturbative QCD, which uses large longitudinal momenta to calculate perturbative factors, & small transverse momenta to limit curve-fit nonperturbative factors.)

String scattering

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