topos approach to quantum mechanics
There are several approaches using
topos theory to formulate and study foundations of quantum mechanics. Some people say “quantum topos theory” what is abit unfortunate as it is not about some quantum analogue of a topos (while such an object may be desired, say in noncommutative geometry), but about using the usual topoi to model quantum mechanics.
The main proposal is from
Chris Isham and his school, see higher category theory and physics.
Andread Doering, C.J. Isham,
A Topos Foundation for Theories of Physics I-IV quant-ph/0703060
Sheaves in quantum topos induced by quantization, arxiv/1109.1192
Kochen-Specker theorem for the topos theoretic interpretation summarizing
Jeremy Butterfield, John Hamilton, Chris Isham, A topos perspective on the Kochen-Specker theorem, I. quantum states as generalized valuations, Internat. J. Theoret. Phys. 37(11):2669–2733, 1998, MR2000c:81027, doi; II. conceptual aspects and classical analogues Int. J. of Theor. Phys. 38(3):827–859, 1999, MR2000f:81012, doi; III. Von Neumann algebras as the base category, Int. J. of Theor. Phys. 39(6):1413–1436, 2000, arXiv:quant-ph/9911020, MR2001k:81016, doi; IV. Interval valuations, Internat. J. Theoret. Phys. 41 (2002), no. 4, 613–639, MR2003g:81009, doi
Another, more recent variant of using topos theory in quantum foundations is due Nijmengen school, see
Bohr topos for detail.
Created on September 7, 2011 17:46:55