Superselection Rules

In General > s.a. canonical quantum mechanics; theta sectors.
* 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 (nontrivial) 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.

References > s.a. [quantum field theory]; measurement.
@ General: Wick et al PR(52), PRD(70); Wightman NCB(95) [review]; Kupsch Pra(98)qp/96; Cisneros et al EJP(98)qp [and 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], a0801 [generalized representatons of nets of C*-algebras and new superselection sectors].
@ Special types of theories: Baumgaertel & Grundling JMP(05)mp/04 [for theories with constraints].
@ Special approaches to quantum mechanics: Colin et al JPA(06)qp/05 [pilot wave].

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 16 jun 2008