Carl Bender: Mathematical Physics

While I was searching the web for more lectures about QFT to complete the course by Cambridge Professor David Tong about the subject (great course, currently on lecture #6, next to review), I happened to visit the web of Perimeter Scholar International or PSI for short (by the Perimeter Institute for Theoretical Physics in Ontario, Canada), and its seminar archive at PIRSA (Perimeter Institute Recorded Seminar Archive). I was delighted to discover that lots of great lectures on Theoretical Physics were available online. Then I decided to start reviewing a course on Mathematical Physics by Professor Carl Bender (Physics Professor at Washington University in St. Louis). At the moment, I have only watched to the first lecture (I also found some of the lectures in YouTube here) about Perturbation Theory and I can say that Professor Bender is a great communicator and makes the subject comprehensible.

As I mentioned before, the videos, notes, mp3… of the course can be found here.

I am quite enthusiast upon the subject and, again, I am pretty sure that I will enjoy it very much.

David Tong: Lectures on Quantum Field Theory

I wish I was born in 2000 or later, I must confess. Why? Because when I was younger (let’s express it this way), there was no YouTube, no lectures on the Web, no nothing but plain text, etc. Nowadays you can follow, for example, a really interesting course on QFT (introductory level) from a Cambridge Professor, for free… This course is the one that I’ve started following. At the moment I’ve only seen the first class of it and hope it doesn’t get very complicated for me with respect to mathematics (not in its best shape of all time at the moment). Professor David Tong explains quite clearly the concepts, so I think I will enjoy the course.

The content of the course (please visit his webpage if you want to know it in detail) treats the following points:

  1. Preliminaries.
  2. Classical Field Theory:   
    Table of Contents; Introduction; Lagrangian Field Theory; Lorentz Invariance; Noether’s Theorem and Conserved Currents; Hamiltonian Field Theory.
  3. Canonical Quantization:   
    The Klein-Gordon Equation, The Simple Harmonic Oscillator; Free Quantum Fields; Vacuum Energy; Particles; Relativistic Normalization; Complex Scalar Fields; The Heisenberg Picture; Causality and Propagators; Applications; Non-Relativistic Field Theory
  4. Interacting Fields:   
    Types of Interaction; The Interaction Picture; Dyson’s Formula; Scattering; Wick’s Theorem; Feynman Diagrams; Feynman Rules; Amplitudes; Decays and Cross Sections; Green’s Functions; Connected Diagrams and Vacuum Bubbles; Reduction Formula
  5. The Dirac Equation:   
    The Lorentz Group; Clifford Algebras; The Spinor Representation; The Dirac Lagrangian; Chiral Spinors; The Weyl Equation; Parity; Majorana Spinors; Symmetries and Currents; Plane Wave Solutions.
  6. Quantizing the Dirac Field:   
    A Glimpse at the Spin-Statistics Theorem; Fermionic Quantization; Fermi-Dirac Statistics; Propagators; Particles and Anti-Particles; Dirac’s Hole Interpretation; Feynman Rules
  7. Quantum Electrodynamics:   
    Gauge Invariance; Quantization; Inclusion of Matter — QED; Lorentz Invariant Propagators; Feynman Rules; QED Processes.

Notes to the course can be found in this pdf (149 pages). The videos that I’m currently watching, in this link.

I want to thank Prof. Tong and the University of Cambridge for this wonderful initiative. By the way, I also hope they extend this (the publishing of the videos) to other courses by Mr Tong (String Theory, Solitons, etc.).