Superselection Rules |

**In General**
> s.a. canonical quantum mechanics; theta 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 CMP(15)-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];
Zych & Greenberger a1906 [mass superselection rule, resolution of puzzle].

@ __Special approaches to quantum mechanics__: Colin et al JPA(06)qp/05 [pilot-wave theory].

@ __Related topics__: Hernández-Coronado FP(12)-a1108 [and quantum Newtonian spacetime].

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send feedback and suggestions to bombelli at olemiss.edu – modified 27 jul 2019