fluctuations in the direction of the condensate. If the field values are identified under a Z2 reflection (corresponding to flipping the sign of all the fields), the superselection sectors are labelled by a nonnegative integer (the absolute value of the topological charge). O(3) charges only make sense in the disordered phase and not at all in the ordered phase. This is because when the symmetry is broken there is a condensate which is charged, which is not invariant under the symmetry group. Conversely, the topological charge only makes sense in the ordered phase and not at all in the disordered phase, because in some hand-waving way there is a "topological condensate" in the disordered phase which randomizes the field from point to point. The randomizing can be thought of as crossing many condensed topological winding boundaries. The very question of what charges are meaningful depends very much on the phase. Approaching the phase transition from the disordered side, the mass of the charges particles approaches zero. Approaching it from the ordered side, the mass gap associated with fluctuations of the topological solitons approaches zero. Examples in particle physics Higgs mechanism In the standard model of particle physics, in the electroweak sector, the low energy model is SU(2) and U(1) broken to U(1) by a Higgs doublet. The only superselection rule determining the configuration is the total electric charge. If there are monopoles, then the monopole charge must be included. If the Higgs t parameter is varied so that it does not acquire a vacuum expectation value, the universe is now symmetric under an unbroken SU(2) and U(1) gauge group. If the SU(2) has infinitesimally weak couplings, so that it only confines at enormous distances, then the representation of the SU(2) group and the U(1) charge both are superselection rules. But if the SU(2) has a nonzero coupling then the superselection sectors are separated by infinite mass because the mass of any state in a nontrivial representation is infinite. By changing the temperature, the Higgs fluctuations can zero out the expectation value at a finite temperature. Above this temperature, the SU(2) and U(1) quantum numbers describe the superselection sectors. Below the phase transition, only electric charge defines the superselection sector. Chiral quark condensate Consider the global flavour symmetry of QCD in the chiral limit where the masses of the quarks are zero. This is not exactly the universe in which we