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Fermionic quantization of knot solitons

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Topological Dynamics in the Physical and Biological Sciences

Knot solitons arise as global energy minimizers in field theories such as the Faddeev-Skyrme model. Such field theories, when quantized, are inherently bosonic because the fundamental fields represent scalar bosons. Nonetheless, the solitons they support can be given fermionic exchange statistics, provided the classical field configuration space has the right algebraic topology. In this talk I will review a computation of the fundamental group of the Faddeev-Skyrme configuration space, and show how this allows a consistent fermionic quantization of knot solitons. This is based on (separate) collaborations with Dave Auckly and Steffen Krusch.

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

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