Spectral presheaves as quantum state spaces | Zendy

Andreas Döring | Zendy

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Spectral presheaves as quantum state spaces

Author(s) -

Andreas Döring

Publication year - 2015

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2014.0247

Subject(s) - mathematics , quantum , pure mathematics , quantum state , operator algebra , quantum operation , hamiltonian (control theory) , spectral theory , operator (biology) , algebra over a field , hilbert space , quantum mechanics , open quantum system , physics , mathematical optimization , biochemistry , chemistry , repressor , transcription factor , gene

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.

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