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Quantum Field Theory 1

PHYS 7325, Fall 2019

Instructor: Professor Jim Halverson

E-mail: [email protected]

Phone: [phone]

Office Hours: Dana 226, TF 8:20-9:50

Grader: Anindita Maiti, [email protected]

Course Information

Course Schedule: Lectures TF 9:50-11:30

Course Location: Ryder 159

Description: The goal of this course is for you to learn the most important elements of quantum field theory, which provides the theoretical framework for numerous systems in condensed matter and high energy physics. There are three parts: Foundations, Renormalization and Symmetry, and Condensed Matter Applications; see below. Foundations is the background material for the other two parts, but it is also of central importance.

Preparation: A strong background in quantum mechanics and classical mechanics is necessary.

Resources: I will lecture from my notes, which have been and will continue to be influenced strongly by the books below. The most the influential books for my notes will be Zee, Altland and Simons, and Peskin and Schroeder. If you are looking to purchase one book, I recommend Altland and Simons if you are a condensed matter student, and Zee otherwise. If you are looking to purchase two books, these are the ones that I recommend. I have found each of the books below to be very useful, though, and am happy to discuss relative strengths of the different texts.

• Quantum Field Theory in a Nutshell (2nd Ed.), A. Zee.
• Condensed Matter Field Theory, A. Altland and B. Simons
• An Introduction to Quantum Field Theory, M. Peskin and D. Schroeder.
• Quantum Field Theory and the Standard Model, M. Schwartz.
• The Quantum Theory of Fields, (I-III), S. Weinberg.
• Quantum Field Theory, M. Srednicki.

Beyond the textbooks, there are also a number of other references that are highly regarded and may be useful in the course or your continuing studies in QFT. This list will be updated as the semester proceeds.

• Applied Conformal Field Theory, by Paul Ginsparg.
• Effective Field Theory and the Fermi Surface, by Joe Polchinski.

Homework and Exams: There will be biweekly homework assignments designed to help guide you through the material. There will a take home final exam, which will involve one or more classic computations in quantum field theory. There will also be an in-class midterm on Friday, November 1. Homework may be a joint effort, but the exams must be your work and yours alone. The texts above may be used on exams.

Late homework policy: Illness and other things come up sometimes, so homework may be turned in within 10 days of the due date, but with a 25% penalty. However, it is strongly recommended to not get behind on the class material in order to complete a past due homework.

Academic Integrity: Be sure to review Northeastern Academic Integrity policies, which are here.

Grading: 40% collaborative homework, 20% in class midterm, 40% final exam.

Course Material

Topics are organized by order of presentation, not by strict adherence to the category.

• Part 1: Foundations. Path integrals; Field Theory; Scalar Field Theory; Origin of Feynman Diagrams; Canonical quantization; Conservation laws and Noether’s theorem; Quantization of the Dirac Field; Lorentz group and Weyl Spinors; Feynman diagrams for fermions; Gauge fields and and the Fadeev-Popov Procedure.

• Part 2: Renormalization and Symmetry. Motivation and regularization; Pauli-Villars and dimensional regularization (epsilon-expansion); Renormalizable vs. Non-renormalizable operators; Physical vs. bare perturbation theory; Renormalization of QED; Quantum effective potential and Coleman-Weinberg; Renormalization group flow; Explicit and spontaneous symmetry breaking; Nambu-Goldstone bosons and Goldstone’s Theorem. Anderson-Higgs mechanism.

• Part 3: Condensed Matter Applications. Non-relativistic Field Theory; O(3) NLSM and antiferromagnetism; Symmetry breaking, topological defects, vortices, and monopoles; Particle-vortex duality; Chern-Simons theory; Conformal Field Theory.

Comments and Recommendations

• Each part of the course will begin with a brief discussion of the central ideas and why they are important.
• Since this material can be quite dense with formalism, each lecture will begin with a concrete outline and an explanation of the basic logic behind the physics presented in the lecture.
• Lecture notes will often be made available to you ahead of time, so I recommend reviewing them prior to lecture so that you can see where we are going. You are free to take your own notes, but it may be more useful to print the lecture notes and pay close attention to the lecture rather than furiously copying off the board. To first approximation, the block letters in the lecture notes will be written on the board, while script writing is for comments I will make.
• During lecture, please ask questions! An interactive classroom will be beneficial to all.
• We will cover a lot of material, and it is important to not get behind. Since homework assignments are biweekly, there will be ample time to ask general questions in office hours that may or may not be related to the homework.
• Undergraduates: Ph.D. level courses differ from undergraduate courses in some important ways. Make sure I discuss these with you.