I have an interest in the mathematics and physics of quantum field theory, the theory underlying the standard model of particle physics. Here are brief syllabii of
related courses I have taught:
Spring 2001, Math 854 Tensor Analysis with Applications
Fall 2002, Math 714 Applied Mathematics
Spring 2003, Physics 701B Elementary Particles
Fall 2004, Math 82C/9Physics 701C The Geometry of Phyiscs
Fall 2005-Spring 2006, Math 941-942, Applied Functional Analysis I and II. The main text for
this course was "Methods of Modern Mathematical Physics, Vol. I, Functional Analysis", by M. Reed
and B. Simon. This course provides background both for students of mathematical analysis and
for anyone interested in the mathematical foundations of quantum mechanics. Later volumes in
this four volume set discuss, e.g., the mathematical foundations of quantum field theory and scattering theory, including Haag-Ruelle scattering for quantum field theory.
Spring 2007, Physics 701B Elementary Particles. Here is an ambitious syllabus
I put together for the course. What actually happened, with the consent of the students, was an brief
introduction to quantum field theory, including the Dirac equation for Bjorken and Drell, v.1,, many details
of canonical quantization and Feynman diagrams for \phi^4 theory from the books by Peskin and Schroeder and
Maggiore, and finally some Feynman rules for QED from Griffith's book; see the references on
page 2