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Fermions coupled to Hopf Solitons

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If you have a question about this talk, please contact Mustapha Amrani.

Topological Dynamics in the Physical and Biological Sciences

Solitons in the Skyrme and the Faddeev-Skyrme model share many similarities. While no topologically non-trivial exact solutions are known in flat space there is a minimal energy charge one soliton on the 3-sphere of sufficiently small radius in both models. The charge one Skyrmion is given by the identity map, whereas the charge one Hopf soliton is given by the Hopf map. Also, the solitons in both models can be semi-classically quantized as fermions, by defining the wave function of the covering space of configuration space and imposing Finkelstein-Rubinstein constraints. When fermions are chirally coupled to Skyrmions the resulting Dirac equation can be solved explicitly on the 3-sphere in the background of a charge one Skyrmion. In this talk, I describe how to couple fermions to Hopf solitons.

This talk is part of the Isaac Newton Institute Seminar Series series.

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