# 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, Jan Schlemmer, Yoh Tanimoto

The aim of the workshop was 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 discussed different points of view on the subject and tried to understand it on a more fundamental level. The workshop provided an opportunity for mathematicians and theoretical physicists to exchange ideas, compare perspectives and get some new insight. The main topics included:

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

The workshop was part of the Junior Hausdorff Program on Mathematical Physics and organized by the group "Local gauge invariance in AQFT".

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.