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 live, where the up and down quarks have a tiny but nonzero mass, but it is a very good approximation, to the extent that isospin is conserved.
Below a certain temperature which is the symmetry restoration temperature, the phase is ordered. The chiral condensate forms, and pions of small mass are produced. The SU(Nf) charges, Isospin and Hypercharge and SU(3), make sense. Above the QCD temperature lies a disordered phase where SU(Nf)×SU(Nf) and color SU(3) charges make sense.
It is an open question whether the deconfinement temperature of QCD is also the temperature at which the chiral condensate melts.
Read more about this topic: Superselection
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