  We explore the space of solutions of the classical equations of motion in the
Euclidean electroweak theory. We sketch a topological prescription that finds
known solutions and indicates the existence of novel ones. All
spatially-varying, time-independent solutions are unstable. However, if we
consider quantum fluctuations around static classical configurations, it may be
possible to find stable solutions called quantum solitons. Such objects carry a
conserved quantum number, in analogy with a topological soliton carrying a
topological charge. We explain the mechanism and motivation for the existence
of a quantum soliton and describe our search for one within a spherical ansatz.
We also comment on promising candidates outside the ansatz.
