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Physics 722, Spring 2021: Quantum Field Theory

Class schedule: T,Th 11am-12:20pm, by Zoom. Zoom link will be emailed prior
to each class.

Office hours: I am always happy to speak with students in the class. I will be mostly at home this semester, so email to arrange a Zoom meeting.

Course webpage: http://physics.wm.edu/~erlich/722S21/

Course material will be posted on Blackboard.
Instructor - Josh Erlich

Small Hall, Room 332B

Office Phone: 757-221-3763

Email: erlich@physics.wm.edu

__Topics to be covered, as space-time permits:__

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- The Born approximation and the Coulomb potential
- Radiative Corrections in QED
- Electron self energy
- Electron vertex function and g-2
- Bremsstrahlung and infrared divergences
- Lamb shift

- Renormalization and the Renormalization Group
- Physical interpretation of running couplings
- Effective field theory

- Symmetries
- Lie groups and Lie algebras
- Isospin, chiral symmetry and hadron phenomenology
- Spontaneous symmetry breaking, Goldstone's theorem
- Anomalous global symmetries

- Gauge Theories
- Functional integral quantization
- Ward-Takahashi Indentities
- Non-Abelian gauge theory (Yang-Mills theory)
- Gauge fixing and Fadeev-Popov ghosts
- Anomalous symmetries
- Quantum Chromodynamics: Asymptotic freedom and confinement
- Electroweak symmetry breaking: the Higgs mechanism
- Standard Model of Particle Physics (introduction)

__Course requirements and grade:__

- Problem sets (70%)
- Take home final exam (30%)

__Text:__
There are quite a few quantum field theory textbooks that emphasize different
aspects of the subject. This course will be loosely based on
M. Peskin and D. Schroeder, *An Introduction to
Quantum Field Theory.* Corrections to the textbook are available here.
I will also provide lecture notes, which have been influenced by a number of sources, most notably Sidney Coleman's lectures. You can find video of Coleman's lectures online here, and lecture notes for the first semester transcribed by Brian Hill here and here, and typeset here. I also borrow from Mehran Kardar's *Statistical Physics of Fields*. David Tong's lecture notes are excellent.
Steven Weinberg's three-book series *The Quantum Theory of Fields* contains insights not found in other textbooks, and is a useful reference.
Matthew Schwartz's book, *Quantum Field Theory and the Standard Model*,
is also excellent.

__Problem sets__

Homework will be assigned roughly weekly on Thursdays, and due the following Thursday. Problem sets will be available on Blackboard.

__Lecture Notes__

Lecture Notes 1 - Introduction, QFT->QM->CM, Coulomb Potential

Lecture Notes 2 - Renormalization

Lecture Notes 3 - Self energy

Lecture Notes 4 - Scalar self energy calculation

Lecture Notes 5 - Fermion self energy

Lecture Notes 6 - Photon self energy, charge renormalization

Lecture Notes 7 - Photon self energy calculation, dimensional regularization

__Problem sets__

Problem Set 1, due Thursday, February 11.

Problem Set 2, due Thursday, February 18.

Problem Set 3, due Thursday, February 25.