Course: PHY509
Instructor: Herman Verlinde
F 2019

Description of Course Goals and Curriculum

By the end of this course, students should have an understanding of the fundamentals of field theory, both classical and quantum, as well as applications of this formalism (largely in particle physics) and its shortcomings.

The first part of the course is dedicated to building up the tools of field theory through path integrals, Green’s functions, Wick’s theorem, and similar essential tools; the first few weeks contain probably the most abstract material presented in the course. The main body of the course is applying these techniques to describe amplitudes for particle processes, i.e. writing particle Lagrangians, drawing Feynman diagrams, evaluating fermion traces, etc. Finally, the last part of the course is dedicated to discussing the refinements and additional considerations that must be made to quantum field theory as it is presented in this course to get a useful theory; here the basics of renormalization are discussed, though not in great detail.

Learning From Classroom Instruction

The course consists of twice-weekly lectures, weekly problem sets, a midterm exam and a final project (final exam optional). Some students found Professor Verlinde’s lecture style and use of board space a bit unusual or difficult to follow, so it is helpful to do at least some reading before lecture to follow the discussion more closely. In particular, each week a chapter of Peskin & Schroeder (course textbook) is assigned, supplemented with notes from David Tong’s QFT course at Cambridge; since the latter is a little less dense and more conversational, it might be helpful to read those notes before lecture, and then read Peskin after lecture after you’re prepared to wade through a more dense and thorough treatment of the material.

It’s also helpful to begin the problem sets as early as possible, since Professor Verlinde discusses material closely related to the problem sets in lecture and is willing to answer specific questions or give hints about the set if you ask a question at the right time.

Learning For and From Assignments

Problem sets are essential for practicing and learning the material. They are challenging; form a study group as early as possible, and attend the once-weekly problem sessions. It is particularly important to thoroughly understand the solutions to these sets early in the course, since these will form the foundation of the material presented later. Most of these problems do not require “clever solutions” or tricks of any kind, but rather require a deep understanding of the fundamentals of the tools you are being asked to use. Especially later in the course it is tempting to discard the rigorous formalism of path integration for the shortcuts presented by using Feynman diagrams, but you’ll make a lot of simple mistakes (factors of 2, minus signs, factors of i) that will harm you in the long run if you forget where these shortcuts are coming from.

The midterm exam is fairly straightforward; it’s a bit long, but otherwise it is a remarkably fair and even-handed assessment of the skills you are expected to have learned in the course. The situation with the final changes from year to year; since many students took the course this year we did short presentations and posters, with some students taking a final exam if they preferred.

External Resources

There are simultaneously very many and very few external resources for learning QFT. On the one hand, there seems to be a lot of information about the subject online, but on the other hand the presentation of the material can vary widely based on whether the presenter is a particle physicist, a statistical physicist, a condensed matter physicist, etc. Therefore it’s essential to be careful with the interpretation of the material you find online. The safest external resource is David Tong’s QFT course at Cambridge; his lecture notes are supplemental reading for the course, and his lecture videos, which are extremely clear and useful, are also available online.

What Students Should Know About This Course For Purposes Of Course Selection

This course is challenging and time-consuming, but rewarding and useful for physicists in many disciplines who have an eye towards graduate study. It is difficult to balance this course with the demands from independent research but not impossible, though it may be helpful to take a slightly lighter courseload than usual to leave enough time for this class. It is difficult to say whether PHY305 is a prerequisite for this course; I don’t think the material covered in PHY305 was essential for understanding the material in this course, though at some points it was useful to have at least seen certain definitions in the past. A strong understanding of the material in PHY208 could potentially suffice.
Quantum Field Theory

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