# Siegel's lectures, PHY 622, F'19

• Fields v4 contains the lecture notes for the class.
• ⚠️ 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.

Topologyin subsectionsbackground material & homework
graph topology
• P−V = L−1
VC2 (last ⅕)
group theory via graphsIB1 (matrices), IC4 (color & flavor)
• index lines
• Feynman graphs
VC9VC9.1 (due 10/28)
1/Ncolor expansion
• color loops
• Euler number
• flavor
VIIC4
worldsheet topology
• duality
• tadpoles
• open→closed
XIA2XIA2.1 (due 11/1)
discrete worldline symmetriesIA4 (proper time)
• CPT
• worldline/spacetime
IA5
string theory typologyIB4-5 (SO/Sp groups)
• Chan-Paton
• worldsheet CPT
• orientation
• supersymmetry
XIA4XIA4.1 (due 11/4)
Geometry
particle propagatorsIIIA1 (Dirac δ), IIIB (classical), VA3 (nonrelativistic)
• proper time
• iε ℞
• energy sign
VB1VB1.1 (due 11/6)
1st-quantized particle graphs
• Schwinger parameters
• 1st-q action
VC8
worldsheet latticesVA5,VB4 (Wick rotation)
• discrete worldsheet
• string action
• preon propagators
XIA7 (1st ½)XIA7.1 (due 11/6)
Particle scattering
1st-q S-matricesIIIB3 (background fields), VA4 (nonrelativistic)
• perturbation
• interaction picture
• Green function
• loops
VIIIC5
Γ functions
• Schwinger parametrization
• Beta function
VIIA2VIIA2.2,3, VIIC2.2 (due 11/11)
Coulomb scatteringIA4 (Mandelstam variables), VA2 (JWKB)
• eikonal approximation
• strong coupling
• infrared
VIIA6 (2nd ½)VIIA6.2 (due 11/13)
String trees
Regge behavior
• ladders
• complex angular momentum
• duality
XIA1XIA1.2 (due 11/15)
Green functions
• cylinder→plane
• closed→open
XIB2 (last ⅖)VIIB1.1 (due 11/15)
Open trees
• 4 tachyons
• limits
• higher-point
XIB6XIB6.2 (due 11/18)
Closed trees
• Schwinger parameters
• 4 tachyons
• open factorization
XIB7XIB7.1,2 (due 11/22)
Green-Schwarz
supersymmetry
• algebra
• positivity
• massless
IIC1
superspace
• coordinates
• covariant derivatives
IIC2
superparticleIIIB1-2 (scalar particle)
• Hamiltonian
• constraints
• lightcone gauge
IIIB6IIIB6.1 (due 11/25)
superstringXIA5 (T-duality)
• currents
• action
• lightcone gauge
XIA9