Siegel's lectures, PHY 622, F'20

⚠️ Any material may be revised during the course.
Fields v4 contains most of 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.
- See also additional notes for the Spinning string.
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).

Free strings

particle	in subsections	background material & homework
constrained systems		IA1 (symmetry)
action constraint algebra gauge field & transformations example: e&m	IIIA5
particle action		IA4 (τ vs. s), IIIA2 (fermions)
Hamiltonian einbein Lagrangian	IIIB1	IIIB1.3 (due 10/5)
gauges		IIIC2, IIB3, IXB3 (lightcone gauge)
covariant (affine) lightcone (unitary)	IIIB2	IIIB2.1 (due 10/7)
background
fields gauge transformations	IIIB3	IIIB3.2 (due 10/7)
bosonic string
action		IXA7 (Weyl scale)
Lagrangian induced metric Hamiltonian boundary conditions	XIA3	XIA3.1,2 (due 10/9)
T-duality		IVA7, IXA5 (⟨g⟩→κ)
background duality symmetry	XIA5	XIA5.1 (due 10/12)
gauges		IB3 (determinants)
conformal lightcone boundaries mass & spin	XIB1	XIB1.3 (due 10/14)
quantization (lightcone)		IIB3-4 (little groups)
oscillators states leading trajectory	XIB2	XIB2.1 (due 10/16)
spinning string
action		VIIB5 (2D spinors & Euclidean)
constraint algebra Hamiltonian Lagrangian	notes
quantization		IIA5 (spinor CPT)
gauges R & NS strings mass & spin GSO projection	notes	"Exercise" (due 10/19)
BRST		IIC3 (graded indices)
nonAbelian algebra cohomology gauge fixing strings	VIA1 notes	VIA1.2 (due 10/23)
string types		VC9 & IA5 (particle)
Chan-Paton worldsheet P & CT supersymmetry	XIA4	VC9.1 (due 10/28)
superstring
supersymmetry
algebra positivity massless	IIC1
superspace
coordinates covariant derivatives	IIC2
superparticle
Hamiltonian constraints lightcone gauge	IIIB6	IIIB6.1 (due 10/30)
superstring
currents action lightcone gauge	XIA9
more particle
conservation
currents gauge fields particles	IIIB4
pair creation
action solution interpretation	IIIB5