nLab Three Roles of Quantum Field Theory


Quantum field theory


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

In May 2011 Graeme Segal gave a series of lectures on the topic of quantum field theory at the Hausdorff Center for Mathematics in Bonn.

  • Graeme Segal, Three Roles of Quantum Field Theory , Felix Klein Lectures 2011, Bonn (website)

    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.

category: reference

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