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 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].

main page – abbreviations – journals – comments – other
sites – acknowledgements

send feedback and suggestions to bombelli at olemiss.edu – modified 18
apr
2016