Professor: Richard Borcherds
Room:TuTh 2-3:30P, 75 EVANS Course control number 54536
Office hours: Tuesday, Thursday 3:30-5:00 927 Evans Hall
This is the course home page (address www.math.berkeley.edu/~reb/275).
The goal of the course is to show how to construct a perturbative quantum field theory from a Lagrangian in a mathematically rigorous way. The topics covered may (or may not) include the Wightman axioms for quantum field theory, time-ordered and composite operators, renormalization, regularization, Feynman measures, infra-red and ultraviolet divergences, BRST symmetry, anomalies, and so on.
The course will not follow a textbook, but will be based on these notes .
There are some notes taken by Anton Geraschenko of a similar short course I gave in fall 2007. There are also some notes taken by Alex Barnard of a course I gave in Fall 2001, though these are rather out of date and the approach taken is rather clumsy.
An introduction to quantum field theory by Peskin and Schroeder. A standard physics text on quantum field theory.
PCT, spin, statistcs and all that, by Streater and Wightman. ISBN-13: 978-0691070629. An introduction to mathematical Quantum Field Theory.
The quantum theory of fields, vols I, II, III, by Steven Weinberg.
Quantum field theory, Itzykson, Zuber. A classic text on quantum field theory. It gives detailed mathematical proofs of several results (such as convergence of Feynman integrals) that are hard to find elsewhere.
Quantization of gauge systems by Henneaux and Teitelboim. This gives an introduction to the antifield formalism, BRST operator, and so on. Also see "Local BRST cohomology in gauge theories" by Glenn Barnich, Friedemann Brandt, Marc Henneaux, hep-th/0002245 .
Diagrammar, by 't Hooft and Veltman. Reprinted in Under the spell of the gauge principle by 't Hooft.
If you want to see a summary of the experimental data see the review of particle physics. You can even order your own (free) paper copy.
The analysis of linear partial differential operators. vol I. Hormander. Contains the distribution theory and material on wave front sets that we use.
Hopf algebras, by E. Abe. ISBN-13: 978-0521604895
Modules over a ring of differential operators. Study of the fundamental solutions of equations with constant coefficients by J. Bernstein. Proves the existence of the Bernstein-Sato polynomial.