# PlanetPhysics/Quantum Logic Topoi

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## Quantum logic topoiEdit

A *\htmladdnormallink{quantum logic* {http://planetphysics.us/encyclopedia/TheoryOfHilbertLattices.html} topos} (*QLT* ) is defined as an extension of the concept of topos in which the Heyting logic algebra (or subobject classifier) of the standard elementary topos is replaced by a *quantum logic* which is axiomatically defined by *\htmladdnormallink{non-commutative {http://planetphysics.us/encyclopedia/AbelianCategory3.html}* and non-distributive} lattice structures.

### RemarkEdit

Quantum logic topoi are thus generalizations of the Birkhoff and von Neumann definition of quantum state spaces based on their definition of a quantum logic (lattice), as well as a *non-Abelian*, higher dimensional extension of the recently proposed concept of a 'quantum' topos which employs the (*commutative* ) Heyting logic algebra as a subobject classifier.

Some specific examples are considered in the following two recent references.

## All SourcesEdit

^{[1]}^{[2]}

## ReferencesEdit

- ↑
Butterfield, J. and C. J. Isham: 2001, Space-time and the philosophical challenges of quantum gravity., in C. Callender and N. Hugget (eds. )
*Physics Meets Philosophy at the Planck scale.*, Cambridge University Press,pp.33--89. - ↑
Butterfield, J. and C. J. Isham: 1998, 1999, 2000--2002, A topos perspective on the Kochen--Specker theorem I - IV,
*Int. J. Theor. Phys*,**37**No 11., 2669--2733**38**No 3., 827--859,**39**No 6., 1413--1436,**41**No 4., 613--639.