Geometric models of matter

Bernd Schroers (Heriot-Watt)

Monday 14th May, 2012 15:00-16:00 204


I will review a proposal to describe static particles in terms of Riemannian 4-manifolds, made in a recent joint paper with Michael Atiyah and Nick Manton (arXiv:1108.5151 and published in Proceedings of the Royal Society A). In this approach, the basic quantum numbers of particle physics (like electric charge or baryon number) are interpreted topologically. For electrically charged particles, the relevant 4-manifolds are non-compact and asymptotically fibred by circles over physical 3-space. This is akin to the Kaluza-Klein description of electromagnetism, except that the roles of magnetic and electric fields are interchanged and that the bundle structure is only assumed asymptotically. I will illustrate the approach by describing the Taub-NUT manifold as a model for the electron and the Atiyah-Hitchin manifold as a model for the proton.

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