Siegel's lectures, PHY 623, S'19

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).

String scattering, etc.

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