**Field Theory**

## Instructor: Mahbub Majumdar

BRACU Class | Date | Time | Room |
---|---|---|---|

PHY 414: Field Theory | T, Th | 3:30-6:00 | UB1-04-?? |

**Synopsis**

This is a first course on quantum field theory. Because some of the audience is somewhat unfamiliar with quantum mechanics, we will take a more mathematical approach. This course is essentially about generating functions, and calculating the coefficients of generating functions. These coefficients can be given a graphical interpretation and are called Feynman Diagrams. Generating functions are easier structures for students to handle because they are a standard tool in combinatorics.

Because of the unusual nature of the course, the syllabus will evolve with the course.

**Marking**

Anybody who understands this course, does the homework, and comes to class very regularly, should get a very good grade. The marking has to be according to BRACU rules, as far as I know. This means

- Attendance: 5%,
- Homework & Quizzes: 25%,
- Midterm 20%,
- Final 50%.

This is an unfortunate grading scale, but it is something which we are required to follow. The most important part of this course is homework and attendance. The quizzes will be just regurgitation of the homework problems. So, anybody who does the homework, will be able to obtain full marks on the quizzes. I don’t want to complicate your life by having silly quizzes, so they will be very easy and come from the homework.

Because, this is a non-standard course, and without a good a teacher, is a rather hard course, you need to attend **EVERY **lecture. I will be very unhappy with students with students who miss lectures. I will be very happy with students who attend all the lectures and are not late.

**Class structure**

Because the only way to understand a course like this is to solve lots of problems, this course will alternate between lecture and recitation class. We will have one long lecture per week. The next class that week will be a recitation where we discuss and work out the homework. Homework will be due either every week or every two weeks.

Course Books

Quantum field theory books are notoriously bad. Standard texts are:

- Peskin & Schroeder (Standard: I had to read this book)
- Schwartz (Standard: I haven’t read it)
- Huang (Really nice book, used at MIT when Huang taught it)
- Maggiore (a bit like Peskin, first chapter is nice)
- Srednicki (I don’t like this book)
- Ramond (The best book)
- Fields by Siegel (The best book if you have time)
- Path Integral Methods in Field Theory by Rivers (I like it a lot)
- Plenty of others like Brown and others

There is also a new book on quantum field theory for undergraduates

- Quantum Field Theory for Gifted Amateurs, by Blundell & Lancaster

We will not use this book, but you may want to consult it for various topics done easily.

The books most relevant for this course are

- Field Theory: A Modern Primer, by Ramond
- Fields by Siegel

They represent the style of the course. I will teach Lorentz invariance from the first chapter of

- Introduction to Supersymmetry by Muller-Kirsten & Wiedemann

And a more mathematical and elegant version of the course is

- Path Integral Methods in Field Theory by Rivers

For calculations we will follow the standard

- Quantum Field Theory by Peskin & Schroeder

If I was teaching a class that it is very comfortable with Quantum Mechanics, I might have instead used the book

- Modern Quantum Field Theory by Banks

It is very concise and is perfect for a lecture course where the instructor explains everything.

Some other resources are the notes by Geroch on QFT which are fantastic and Tong’s Cambridge Part III Notes for QFT and t’Hooft’s short notes on QFT. A nice book doing all of this using some cleaner mathematics is Mathematical Aspects of Quantum Field Theory by de Faria & de Melo. Zee’s book “Quantum Field Theory in a Nutshell,” is also very nice. There are numerous other reviews from various summer schools or notes by teachers.

Nowadays, a student’s best friend is YouTube. You can learn almost anything from YouTube or various other online resources. Some very useful lectures online are:

- Sidney Coleman’s online lectures from way back when
- David Tong’s lectures on Quantum Field Theory.
- Lots and lots of other stuff online…

Some background material for the course on special relativity and generating functions are

A wonderful popular science introduction to Quantum Field Theory is

This should be the first book you read before coming to class.

**Lecture Notes**

- Lecture Notes 1: Relativity, Lorentz Transformations and More…
- Lecture Notes 2: Irreducible Representations of the Poincare Group and Particles…

**Preliminary Reading & Viewing**

- Preliminary Reading: The Infinity Puzzle by Frank Close
- Preliminary Viewing: David Tong Cambridge Lectures on QFT

**Lectures**

- Lecture 1: Special Relativity
- Reading: Chapter 1, Special Relativity by Rindler
- Homework: Odd problems, Rindler Chap 1
- Homework 1 Solutions

- Lecture 2: Lorentz Transformation in Matrix Form
- Reading: Chapter 5, Special Relativity by Woodhouse
- Homework: Index manipulation
- Homework 2 Solutions

- Lecture 3: EXP representation and Lie Algebras
- Reading: Chapter 2, Lie Algebras by Georgi
- Homework 3: EXP and Heisenberg

- Lecture 4: The Rotation Group SO(3)
- Reading: Chapter 8, Special Relativity by Schwarz
- Homework 4: Rotations
- Midterm (password protected)

- Lecture 5: Differences between the Rotation Group and the Lorentz Group
- Reading: Chapter 8, Special Relativity by Schwarz
- Reading: Chapter 1: Muller-Kirsten, Wiedemann, Supersymmetry

- Lecture 6: Generators for the Lorentz Group and its Lie Algebra
- Lecture 7: Representations of the Poincare Group and Induced Representations
- Lecture 8: A Homomorphism from the Lorentz Group to SU(2)
- Lecture 9: What Do Spinors exist? What are they?
- Lecture 10: How Do Spinors Transform under the Lorentz Group?
- Lecture 11: Spinor invariants
- Lecture 12: Supersymmetry
- Lecture 13: Twistors