We show that the configuration space of the classical, bosonic Weinberg-Salam theory has a non-contractible loop. This probably implies that there is an unstable, static, finite-energy solution of the field equations. Its energy is the height of the barrier for tunneling between "topologically distinct" vacuums. We establish an upper bound on this energy of order 10 TeV.
N. S. Manton (Sat,) studied this question.