Workshop: Algebraic Quantum Field Theory and Local Symmetries

Date: September 26 - 28, 2012
Venue: HIM lecture hall, Poppelsdorfer Allee 45
Organizers: Wojciech Dybalski, Katarzyna Anna Rejzner, Yoh Tanimoto, Jan Schlemmer

The aim of the workshop is to gather researchers with expertise both in the operator algebraic and the perturbative approach to quantum field theory in order to investigate some problems concerning the local gauge invariance. We want to discuss different points of view on the subject and try to understand it on a more fundamental level. The workshop will provide an opportunity for mathematicians and theoretical physicists to exchange ideas, compare perspectives and get some new insight. The main topics will include:

- Algebraic quantum field theory (AQFT)
- QFT on curved spacetimes,
- Gauge theories and Seiberg dualities,
- Locally covariant quantum field theory and perturbative AQFT

The workshop is a part of a Junior Hausdorff Trimester Program and is organized by the group "Local gauge invariance in AQFT". We hope to get a resonance also from the the other participants of the Hausdorff Program, since the topics we are proposing cover a wide range of dynamically developing research areas in mathematics and theoretical physics. The detailed schedule, as well as the list of speakers, will appear soon. Below we provide a short description of the workshop main topics.
Local gauge invariance has proven to be a powerful principle, guiding the development of quantum field theory. Its significance is confirmed by the great predictive power of the Standard Model. It also has a very natural geometric formulation at the level of classical field theory. However, it is not known whether it retains an intrinsic meaning after the process of quantisation or is rather an accidental property. As a matter of fact, the physics literature suggests the latter possibility: It gives examples of quantum field theories which have several classical counterparts with different local gauge symmetries.
The algebraic quantum field theory (AQFT) has a long tradition in investigating the mathematical foundations of QFT. It provides an axiomatic setting that allows to treat quantum field theories on a very general level. This way many important results could be proven.
One of the most prominent examples is the theory of superselection sectors, which provides a way to analyze the consequences of a global gauge symmetry. Recently a lot of progress has been made in applying the ideas of AQFT also in the perturbative setting. This approach turned out to be very successful in understanding the QFT on curved spacetime, in particular the problem of renormalization. Recently also the gauge theories were incorporated into this framework.

The schedule will be announced in time.