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quantum logic topoi
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Definition 1.1 A quantum logic 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 logicwhich is axiomatically defined by non-commutative and non-distributive lattice structures.
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.
- 1
- 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.
- 2
- 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.
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"quantum logic topoi" is owned by bci1.
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| Other names: |
quantum logics toposes |
| Also defines: |
generalized quantum topos |
| Keywords: |
quantum logics toposes |
Cross-references: Heyting logic algebra as a subobject classifier, quantum topos, non-Abelian, quantum state spaces, non-commutative, elementary topos, concept, topos, quantum logic
This is version 8 of quantum logic topoi, born on 2009-01-11, modified 2009-01-31.
Object id is 376, canonical name is QuantumLogicTopoi.
Accessed 1542 times total.
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Pending Errata and Addenda
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