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 $S^2$. 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.

References in corpus (2)

• Analysis of the Faddeev model
• The Pontrjagin-Hopf invariants for Sobolev maps

Cited by in corpus (10)

• Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes
• Analytic self-gravitating $4$-Baryons, traversable NUT-AdS wormholes, flat space-time multi-Skyrmions at finite volume and a novel transition in the $SU(3)$-Skyrme model
• SU(N) Multi-Skyrmions at Finite Volume
• Fermionic quantization of Hopf solitons
• Cosmological Einstein-Skyrme solutions with non-vanishing topological charge
• Multi-Skyrmions with orientational moduli
• Bianchi IX cosmologies in the Einstein-Skyrme system in a sector with non-trivial topological charge
• Homogeneous spaces and Faddeev-Skyrme models
• Gauge theory of Faddeev-Skyrme functionals
• Homotopy classification of maps into homogeneous spaces