**Math 405: Mathematical Physics: Spring 2016**

This is a modern mathematical physics course focusing on mathematical physics techniques used in theoretical physics. It will provide the mathematical tools needed to understand the Gauge/Gravity Duality. This course is a culmination of the other courses I have taught: Group Theory, Field Theory and General Relativity.

**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%.

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**

You will be expected to write up summaries of the topics we cover in class to turn is as homework. You will also be expected to complete all of the homework.

Course Book:

- Ammon, Erdmenger, Gauge/Gravity Duality, Cambridge University Press 2015.

For the quantum field theory we will use you may want to consult

- 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

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.

**Mathematical Physics**

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

MAT 405: Field Theory | Su, Tue | 5:15 - 8:00 | UB2-1102 |

**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