### Segal on *Three roles of quantum field theory*

#### Posted by Urs Schreiber

This May Graeme Segal will give the *Felix Klein Lectures* at the Hausdorff Center for Mathematics in Bonn.

**Three roles of quantum field theory**

May 2 - 18

**Abstract** Quantum field theory has many roles, and the lectures will be about three of them. The primary role is to provide a description of all of fundamental physics when gravity is firmly excluded. A second, at first surprising, role has emerged from string theory, which is a theory of gravitation: it turns out that a two-dimensional field theory can be regarded as a generalized manifold, and in particular can be a model for space-time. Thirdly, quite apart from physics, the concept of a field theory has taken on a new life as an organizing principle in other areas of mathematics - not only in geometry and representation theory, but even in connection with quantum computing.

The three roles can be seen together as aspects of noncommutative geometry, and that will be a central theme of the lectures. The talks will aim to show how powerful the field theory idea is by jumping between a variety of contexts, beginning from the origins of the structure in particle physics, with a little about so-called “Wick rotation”, and then moving towards more pure-mathematical applications to analysis, algebra, and the structure of manifolds.

Posted at April 14, 2011 12:20 AM UTC
## Re: Segal on Three roles of quantum field theory

Graeme Segal wrote:

How important is the number 2 here? Is there a reason why 1d or 3d field theories

can’tbe regarded as generalized manifolds?