Categorical Quantum Models and Logics

Download or read book Categorical Quantum Models and Logics written by Chris Heunen and published by Amsterdam University Press. This book was released on 2009-11-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies the logic behind quantum physics, using category theory as the principal tool and conceptual guide. To do so, principles of quantum mechanics are modeled categorically. These categorical quantum models are justified by an embedding into the category of Hilbert spaces, the traditional formalism of quantum physics. In particular, complex numbers emerge without having been prescribed explicitly. Interpreting logic in such categories results in orthomodular property lattices, and furthermore provides a natural setting to consider quantifiers. Finally, topos theory, incorporating categorical logic in a refined way, lets one study a quantum system as if it were classical, in particular leading to a novel mathematical notion of quantum-