Superselection

In Quantum mechanics, superselection extends the concept of selection rules.

Superselection rules are postulated rules forbidding the preparation of quantum states that exhibit coherence between eigenstates of certain observables. It was originally introduced by Wick, Wightman, and Wigner to impose additional restrictions to quantum theory beyond those of selection rules.

Mathematically speaking, two quantum states and are separated by a selection rule if for any given Hamiltonian, while they are separated by a superselection rule if for all physical observables .

A superselection sector is a concept used in quantum mechanics when a representation of a *-algebra is decomposed into irreducible components. It formalizes the idea that not all self-adjoint operators are observables because the relative phase of a superposition of nonzero states from different irreducible components is not observable (the expectation values of the observables can't distinguish between them).