The Born rule as structure of spectral bundles (extended abstract)
Category Theory
2012-10-03 v1 Quantum Physics
Abstract
Topos approaches to quantum foundations are described in a unified way by means of spectral bundles, where the base space is a space of contexts and each fibre is its spectrum. Differences in variance are due to the bundle being a fibration or opfibration. Relative to this structure, the probabilistic predictions of the Born rule in finite dimensional settings are then described as a section of a bundle of valuations. The construction uses in an essential way the geometric nature of the valuation locale monad.
Keywords
Cite
@article{arxiv.1210.0615,
title = {The Born rule as structure of spectral bundles (extended abstract)},
author = {Bertfried Fauser and Guillaume Raynaud and Steven Vickers},
journal= {arXiv preprint arXiv:1210.0615},
year = {2012}
}
Comments
In Proceedings QPL 2011, arXiv:1210.0298