  In this paper we show how to quantize Hopf solitons using the
Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if
their Hopf charge is odd. Symmetries of classical minimal energy configurations
induce loops in configuration space which give rise to constraints on the wave
function. These constraints depend on whether the given loop is contractible.
Our method is to exploit the relationship between the configuration spaces of
the Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then use
recent results in the Skyrme model to determine whether loops are contractible.
We discuss possible quantum ground states up to Hopf charge Q=7.
