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], CMP(09)-a0801 [generalized
representatons of nets of C*-algebras and new topological superselection sectors].
@ Special types: 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].
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