Course Syllabus

Quantum Field Theory is a beautiful subject. It provides an extremely powerful set of computational methods that have yet to find any fundamental limitations. It has led to the most fantastic agreement between theoretical predictions and observed experimental results. Yet the subject is a mess. Its foundations are flimsy. It can be absurdly complicated. And it is most likely incomplete. There are often many ways to solve the same problem whose equivalence is obscure at best. This leaves a formidable challenge for the design and presentation of an introduction to the subject.

The approach I will take in this course is to emphasize that Quantum Field Theory is first and foremost a tool for performing practical calculations. In this regard, I will try to emphasize the physical problems which have driven the historical development of the field, and to show how they can be solved. For most problems, there is a direct solution, where one can appreciate and apply physical intuition, and also a fancy quick mathematical solution, which gives the same answer. It is often extremely difficult to decipher why these two (or more) solutions agree. Some of the fancy techniques, such as Feynman Path Integrals, are so powerful that we must use them for certain applications. In the end, a successful field theorist must have strong physical intuition but also control of the modern mathematical approaches. I will do my best to teach both.

It is often said that Quantum Field Theory is a course which is its own prerequisite. That happens because you usually learn a lot of complicated formalism first and don’t get to the physical problems until well into the course. When you do start calculating things, you begin to ask what it all means and why your answers are turning out right. Then you have to go back and relearn the formalism so that it makes sense. That is why it takes two passes. This seems like a silly way to go about it. A better approach seems to be introducing the necessary formalism as we go along without dwelling on the fine points. Interested students who want to become theorists can, and should, study the fine points for the second pass. But probably not everyone who wants to learn field theory is in that category. Instead, we will try to connect to experiments whenever possible, mostly through the problem sets. I hope that by connecting the formal aspects of field theory directly to their use in applications, the material will simplify. Quantum Field Theory is not a monster, it is just a misunderstood and unconventionally beautiful work in progress.

This course is designed to be of interest and accessible to any graduate student in physics, and to undergraduates who have taken a full year of quantum mechanics and are very comfortable with mathematics. The course is flexible -- students interested in topics as diverse as chemistry, mathematics, astronomy, atomic molecular or optical physics, condensed matter physics, experimental particle physics and string theory will take different things out of it. More formal/theoretically minded students can focus on the more formal elements, while experiment-oriented students can focus on practical applications. If you have any questions about whether the course is appropriate for you, please come talk to me.

Although the course should be accessible to a wide audience, it will be a disaster for anyone who does not have sufficient time to come to class, read the book, study the examples, do the problem sets, and work with the teaching staff. Students typically devote 20 hours/week to the class. If you do not have that kind of space in your schedule, do not take the class.

Textbook:

The textbook for this course is Quantum Field Theory and the Standard Model by me (Schwartz 2014). 

Course Meeting Place:

  • T/Th 1:30-2:45 in Jefferson 356 

Office hours:

  • Schwartz: Tuesday 11-12 in J455
  • Schwartz: Friday 3-4 in J455
  • Alek Bedroya: Monday 1:30 pm - 2:30 pm in J 356
  • Alek Bedroya: Tuesday 4:30 pm - 5:30 pm in Science Center 105
  • Grader: Brian Warner

Sections:

  • Thursday 5 pm - 6 pm in J356
  • Friday 9 am - 10 am in J256 

Grading:

  • 60% weekly problem sets, 30% take home final
  • 10% for participation. This means asking questions in class, in office hours and in sections. Communication is critical to success in physics.
  • Many problem sets will have some problems marked with a *. These problems are supposed to be a little harder or a little deeper than the main track problems. Everyone is encouraged to do all the problems, but only the non-* ones are required to complete the course. The * ones will be considered extra credit.

Problem sets:

  • The problem sets in this course are hard and time-consuming. They are also absolutely critical to understanding the material, perhaps more so in this course than in any other course you have taken. Expect to take up to 20 hours a week working on the problem sets.
  • Due at 5pm Wednesday either by submission on this site or dropped in Alek's mailbox.
  • Late problem sets will be fined 5 points per day.
  • The lowest pset score will not be dropped. Do them all.

Final:

  • The final exam will be a 48 hour take home exam.
  • You can download it at noon on Dec 11  (wed) and it is due at noon on Dec 13 (Fri).

Quiet questions:

  • If you have questions in class and want to ask them anonymously, please write them at bit.ly/253a-2019

 

Lecture Schedule: 

 

Module

Class
#

Date

Topic

Chapter in Schwartz

Supplementary Material


1

1

Sep 3

Quantum Theory of Radiation

Chapter 1

Pais (various parts)

2

Sep 5

Lorentz invariance, Second Quantization

Chapter 2

 

3

Sep 10

Classical field theory

Chapter 3

 

4

Sep 12

Peskin 4.5, 1

5

Sep 17

Cross sections

Chapter 5

Srednicki 5, Peskin 7.2

6

Sep 19

The S-matrix

Chapter 6

 

7

Sep 24

Feynman rules

Chapter 7

Peskin 4.2-4.4

8

Sep 26

2

9

Oct 1

Spin 1 particles and the Poincare group

Chapter 8

Peskin 2.3

Weinberg 2.4,2.5, 5.3,13.1

10

Oct 3

Gauge invariance

11

Oct 8

Scalar QED

Chapter 9

Srednicki 61, Weinberg 13.1

12

Oct 10

Spinors

Chapter 10

Srednicki 33-36

13

Oct 15

Spinor solutions and CPT

Chapter 11

Weinberg 3, 4, 5

14

Oct 17

Spin and Statistics

Chapter 12

 

15

Oct 22

QED

Chapter 13

Peskin 5

16

Oct 24

17

Oct 29

Path Integrals

Chapter 14

Peskin 9

18

Oct 31

3

19

Nov 5

The Casimir effect

Chapter 15

Zee 1.9, Casimir's papers

20

Nov 7

Vacuum polarization

Chapter 16

Peskin 7

21

Nov 12

22

Nov 14

Electron magnetic moment

Chapter 17

Peskin 6

23

Nov 19

Mass renormalization

Chapter 18

Peskin 7.1

24

Nov 25

Renormalized Perturbation Theory

Chapter 19

Peskin 6.3

25

Nov 28

Renormalizability

Chapter 21

Weinberg 12

26

Dec 3

Non-renormalizable theories

Chapter 22

Weinberg 12

 

Course Summary:

Date Details