Fermionic quantization and configuration spaces for the Skyrme and Faddeev-Hopf models
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 . 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.
Keywords
Cite
@article{arxiv.hep-th/0411010,
title = {Fermionic quantization and configuration spaces for the Skyrme and Faddeev-Hopf models},
author = {Dave Auckly and Martin Speight},
journal= {arXiv preprint arXiv:hep-th/0411010},
year = {2015}
}