  Description of electrons as solitons of the polarization field implies that
an ordinary dielectric has a hidden order, associated with the invariance with
respect to adding loops of quantized electric flux. We describe the mechanism
by which the finite polarizability of the medium renders the interaction
between the solitons short-ranged (prior to their coupling to electromagnetism)
and argue that the structure of the solitons allows them to be quantized as
either fermions or bosons. At the quantum level, the theory has, in addition to
the solitonic electric, elementary magnetic excitations, suggesting that small
dielectrics may host quantized magnetic vortices carrying circular polarization
currents.
