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In this paper we show how to quantize Hopf solitons using theFinkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions iftheir Hopf charge is odd. Symmetries of classical minimal energy configurationsinduce loops in configuration space which give rise to constraints on the wavefunction. These constraints depend on whether the given loop is contractible.Our method is to exploit the relationship between the configuration spaces ofthe Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then userecent results in the Skyrme model to determine whether loops are contractible.We discuss possible quantum ground states up to Hopf charge Q=7.Comment: 22 pages, no figures. Minor corrections: final published versio

Fermionic Quantization of Hopf Solitons