Masterclass by Nicolai Reshetikhin (UC Berkeley)

Title: Perturbative quantization of gauge theories on manifolds with boundary

2015.08.05 | Jane Jamshidi

Date Mon 09 Nov Fri 13 Nov
Time 09:30    16:00
Location Aarhus University, Denmark
Registration has closed

Gauge theories are one of the central themes of modern theoretical physics and of many areas in geometry. Quantization of classical field theories remain one of the central subjects in mathematical physics. Here the main problem is quantization of Yang-Mills theory which would meet physical expectations, such as confinement. Perturbative quantization where the answers are given by formal power series with coefficients being sums of Feynman diagrams, so far remain the main tool for working with gauge theories. The most general scheme of perturbative quantization when the spacetime does not have a boundary is the Batalin-Vilkovisky(BV) approach which generalizes the Faddeev-Popov and BRST quantizations. 

The non-perturbative quantization of a gauge theory was constructed for the Chern-Simons theory1,2 and for the two-dimensional Yang-Mills theory3. One of the main concepts in topological quantum field theory (TQFT) is the functorial point of view coined by Atiyah and Segal which considers as a functors from a category of cobordims to the category of vector spaces. This has been extended recently to higher categories.


The goal of these lectures is an outline of how to develop the BV quantization of gauge theories on
spacetime manifolds with boundary and how to fit this into a funtorial picture in the Atiyah-Segal style.

Main examples will be BF theories and their perturbations.

The lectures are based on joint work with A. Cattaneo and P. Mnev.

1) Witten, E., Quantum field theory and the Jones polynomial. Comm. Math. Phys. 121 (1989), no. 3, 351--399.

2) Reshetikhin, N.; Turaev, V. G. Invariants of $3$-manifolds via link polynomials and quantum groups. Invent. Math. 103 (1991), no. 3, 547--597.

3) Witten, E., On quantum gauge theories in two dimensions, Comm.Math.Phys. 141 (1991) 153--209.

4) Alberto S., Cattaneo; Pavel, Mnev; Nicolai, Reshetikhin, Classical BV theories on manifolds with boundary,
Commun. Math. Phys. 332, 535–603 (2014), arXiv:1201.0290 [math-ph].

5) Alberto S., Cattaneo; Pavel, Mnev; Nicolai, Reshetikhin, Perturbative quantization of gauge theories on manifolds with boundary, in preparation.


Social programme

  • Monday 9/11 at 6pm: Social networking incl. light supper. Free of charge.
  • Thursday 12/11 at 6pm: Special dinner at a restaurant in town. This costs DKK 375 (three course meal incl. a wine menu). Registration will be possible from 1 October. 

 Included in the event

  • Morning and afternoon coffee/tea
  • Lunches on weekdays
  • Social dinner (first night)

In special cases, QGM is able to offer support for accommodation to junior researchers (PhD students and postdocs). Only applications received before 1 October 2015 will be considered. 

Jørgen Ellegaard Andersen (QGM, AU)


List of participants
Andersen, Jørgen Ellegaard (QGM, AU)
Arkhipov, Sergey (AU) 
Deividas, Sabonis (University of Copenhagen)
Gekas, Stephanos (Aristotle Univ. of Thessaloniki) 
Kramer, Reinier, (Korteweg-de Vriesinstituut, Universiteit van Amsterdam)
Li, Qiongling (AU) 
Malusa, Alessandro (QGM, AU)
Meneses, Claudio (CIMAT) 
Niemimäki, Ossi (University of Helsinki)  
Lorand, Jonathan (University of Zurich)
Petersen, William E. (QGM, AU)
Poulsen, Niccolo (QGM, AU)
Romao, Nuno (University of Göttingen)
Sadrolashrafi, Afsaneh 
Schiavina, Michele (UZH) 
Stolin, Alexander (Chalmers/University of Gothenburg) 
Vishnyakova, Liza (Max Planck Institute, Bonn)
Weelinck, Tim (University of Edinburgh)
Wernli, Konstantin (University of Zurich) 
Youmans, Donald (Max Planck Institute, Bonn)

Video recordings of the lectures