quantum logic topoi
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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