Fermionic quantization of Hopf solitons

Details Fermionic quantization of Hopf solitons Fermionic quantization of Hopf solitons

2005-03-07

arxiv.org/abs/hep-th/0503067v2

Commun.Math.Phys. 264 (2006) 391-410

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, no figures. Minor corrections: final published version

Scientific paper

10.1007/s00220-005-1469-4

In this paper we show how to quantize Hopf solitons using the Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if their Hopf charge is odd. Symmetries of classical minimal energy configurations induce loops in configuration space which give rise to constraints on the wave function. These constraints depend on whether the given loop is contractible. Our method is to exploit the relationship between the configuration spaces of the Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then use recent results in the Skyrme model to determine whether loops are contractible. We discuss possible quantum ground states up to Hopf charge Q=7.

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