Topics course in topology:
Batalin-Vilkovisky formalism and applications in topological quantum field theory.
Fall 2016, University of Notre Dame
MATH 80430
Instructor: Pavel Mnev
Syllabus.
Lecture notes. (So far: lectures 1-23)
Useful references:
For symplectic view on classical field theory: our paper with A.S. Cattaneo and N. Reshetikhin: "Classical and quantum Lagrangian field theories with boundary" (2012)
- has lots of examples, written like a survey/introduction to the subject.
Etingof's lecture notes for the course "Mathematical ideas and notions of quantum field theory" (2002).
- A very good reference on Feynman diagram technique for finite-dimensional integrals.
Reshetikhin's notes "Lectures on quantization of gauge systems" (2010).
- A comprehensive discussion of Feynman diagram technique for
stationary phase-type integrals on supermanifolds, with an application
to gauge systems treated by Faddeev-Popov construction.
On Berezin integral: Andrei Losev, "From Berezin integral to Batalin-Vilkovisky formalism: a mathematical physicist's point of view" (2007).
- A very inspiring non-technical discussion of integration on superspaces and why one should care about it.
Concerning divergencies of Feynman graphs and renormalization:
M. Peskin, D.Schroeder, "An introduction to quantum field theory," (1995).
- A standard easy-going reference for physics students.
K. Costello, "Renormalization and effective field theory," Vol. 170, AMS (2011). (A shorter preliminary version on arXiv: "Renormalisation and the Batalin-Vilkovisky formalism", 2007.)
- An interpretation of Wilson's picture of renormalization (i.e.
renormalization viewed as a flow from high-energy theories to
low-energy theories).