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superselle
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There are 10 letters in SUPERSELLE ( E1L1P3R1S1U1 )
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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 * * * * * ψ * * 1 * * * * * {\displaystyle \psi _{1}} * and * * * * * ψ * * 2 * * * * * {\displaystyle \psi _{2}} * are separated by a selection rule if * * * * ⟨ * * ψ * * 1 * * * * | * * H * * | * * * ψ * * 2 * * * ⟩ * = * 0 * * * {\displaystyle \langle \psi _{1}|H|\psi _{2}\rangle =0} * for any given Hamiltonian * * * * H * * * {\displaystyle H} * , while they are separated by a superselection rule if * * * * ⟨ * * ψ * * 1 * * * * | * * A * * | * * * ψ * * 2 * * * ⟩ * = * 0 * * * {\displaystyle \langle \psi _{1}|A|\psi _{2}\rangle =0} * for all physical observables * * * * A * * * {\displaystyle A} * . * 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). |