Topics course in topology:

Batalin-Vilkovisky formalism and applications in topological quantum field theory.

Fall 2016, University of Notre DameBatalin-Vilkovisky formalism and applications in topological quantum field theory.

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).