Abstract
The fundamental group and rational cohomology of the configuration spaces of the Skyrme and Faddeev-Hopf models are computed. Physical space is taken to be a compact oriented 3-manifold, either with or without a marked point representing an end at infinity. For the Skyrme model, the codomain is any Lie group, while for the Faddeev-Hopf model it is S 2. It is determined when the topology of configuration space permits fermionic and isospinorial quantization of the solitons of the model within generalizations of the frameworks of Finkelstein-Rubinstein and Sorkin. Fermionic quantization of Skyrmions is possible only if the target group contains a symplectic or special unitary factor, while fermionic quantization of Hopfions is always possible. Geometric interpretations of the results are given.
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Communicated by L. Takhtajan
The first author was partially supported by NSF grant DMS-0204651
The second author was partially supported by EPSRC grant GR/R66982/01
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Auckly, D., Speight, M. Fermionic Quantization and Configuration Spaces for the Skyrme and Faddeev-Hopf Models. Commun. Math. Phys. 263, 173–216 (2006). https://doi.org/10.1007/s00220-005-1496-1
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DOI: https://doi.org/10.1007/s00220-005-1496-1