Quantum Field Theory Seminar (Spring 2011 -- Spring 2012)
Kevin Costello's mathematical notion of
Perturbative Quantum Field Theory.

All of Costello's work on this topic is available on his web page

http://www.math.northwestern.edu/~costello
(say, under ``Renormalization'').

1. The basic text is Costello's book ``Renormalization and effective field theory'' on mathematical foundations of perturbative quantum field theory. We are interested in chapters 1,2 and 5.

Here are the first two chapters of the book:
• Chapter 1.
• Chapter 2.

2. The algebraic aspect of Costello's mathyematical formalism of perurbative QFT is found in the text ``Factorization algebras in perturbative quantum field theory'', with Owen Gwilliam.
This appears in a form of a wiki, so some elementary thought is required in order to print the text without many ugly repetitions. [On the Contents list click the topics that you are interested in. The section that is clicked will appear beneath the content list. Notice that in order to collect the sections in the correct order, you should acquire them in the OPPOSITE order, i.e., one should start with the last topic of interest. 3. One example of how factorization algebras are used is in three papers of Costello on ``Geometric construction of the Witten genus.'' TIME:

Mondays at 4:00 in 1322 LGRT.

SEMINAR NOTES (unfortunately just a transitional form):

• Perturbative QFT notes

Additional notes:

These are extra notes on some topics that may be mentioned but not covered in detail.
• 1. From Classical Mechanics to QFT for absolute begginners    These are notes on Classical and Quantum Mechanics for absolute begginers.
• 2a. Dictionary (physics terminology).    This is a list of short definitions of some standard notions.
• 2b. Some Things Phycists Do,    The same but fewer definitions with more explainations.
• Super math notes (old) Sections 1-4 largely follow Deligne-Morgan notes on Bernstein lectures. The rest are various remarks and speculations. The ``super math'' is the background for the ``super'' part of supersymmetry (the remaining ingredient are spinors).