title: Spectral presheaves as quantum state spaces.
abstract: For each quantum system described by an operator algebra [Formula: see text] of physical quantities, we provide a (generalized) state space, notwithstanding the Kochen-Specker theorem. This quantum state space is the spectral presheaf [Formula: see text]. We formulate the time evolution of quantum systems in terms of Hamiltonian flows on this generalized space and explain how the structure of the spectral presheaf [Formula: see text] geometrically mirrors the double role played by self-adjoint operators in quantum theory, as quantum random variables and as generators of time evolution.
authors.affiliation: Institute of Theoretical Physics I, Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany andreas.doering@fau.de.
authors.forename: Andreas
authors.initials: A
authors.lastname: Döring
keywords: category; flow; operator algebra; state space; topos