Isaac Newton Institute for Mathematical Sciences

Quantum principal bundles in twistor theory

13th September 2006

Author: Brain, S (University of Oxford)

Abstract

I shall discuss some examples of principal bundles appearing in mathematical physics, in particular the familiar family of Hopf fibrations and the principal bundles associated to instantons on conformal space-time. These bundles have a very natural description in terms of non-commutative (and, where necessary, non-associative) geometry. Indeed, the Hopf bundles are seen to possess a uniform presentation when viewed as quantum bundles. The bundles appearing in the Penrose-Ward transform are also easily constructed. Both families of principal bundles then submit to functorial quantization via a cocycle twist. I shall discuss some of the ways in which this is possible.