Fermionic Quantization and Configuration Spaces for the Skyrme and Faddeev-Hopf Models |
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Authors: | Dave Auckly Martin Speight |
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Institution: | (1) Department of Mathematics, Kansas State University, Manhattan, Kansas 66506, USA;(2) School of Mathematics, University of Leeds, Leeds, LS2 9JT, England |
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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 S2. 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.
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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