In General > s.a. canonical quantum
sectors; Superposition Principle.
* Idea: A statement that singles out some unit rays in a Hilbert space as not physically realizable, in operator quantum mechanics; Mathematically, they "are" the (non-trivial) center of the Lie algebra of observables.
* Remark: If they commute (e.g., when there is a complete set of commuting observables) they imply that the Hilbert space can be decomposed into a direct sum of superselection sectors, on which the other observables act irreducibly; A physical state cannot be a superposition of states belonging to different sectors (and the projection operators on these are not observables).
* Types: "Hard", kinematically rooted; "Soft", induced by dynamical decoherence.
> Online resources: see Wikipedia page.
References > s.a. quantum field theory / measurement
in quantum theory.
@ General: Wick et al PR(52), PRD(70); Wightman NCB(95) [review]; Kupsch Pra(98)qp/96; Cisneros et al EJP(98)qp [and the superposition principle]; Giulini LNP(00)qp [hard and soft]; Ojima mp/02, mp/02 [general framework]; Hall JPA(04)qp [types, from constraints]; Giulini a0710-in [rev].
@ Symmetries, decoherence: Giulini et al PLA(95)gq/94; Giulini LNP(00)qp/99.
@ In curved spacetime: Ashtekar & Sen JMP(80) [due to spacetime topology]; Guido et al RVMP(01)mp/99; Brunetti & Ruzzi CMP(07)gq/05 [and general covariance], CMP(09)-a0801 [generalized representatons of nets of C*-algebras and new topological superselection sectors]; Vasselli a1211 [as categories of sections of presheaves of symmetric tensor categories].
@ Special types: Aharonov & Susskind PR(67) [charge superselection rule]; Baumgaertel & Grundling JMP(05)mp/04 [for theories with constraints]; Ciolli RVMP(09) [2D massless free scalar field].
@ Special approaches to quantum mechanics: Colin et al JPA(06)qp/05 [pilot-wave theory].
@ Related topics: Hernández-Coronado a1108 [and quantum Newtonian spacetime].
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