title: The geometric semantics of algebraic quantum mechanics.
abstract: In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
authors.affiliation: Instituto Nacional de Matemática Pura e Aplicada, IMPA, Estrada Dona Castorina 110, Rio de Janeiro 22460-320, Brazil alekosandro@gmail.com jacruzm@impa.br.
authors.forename: John Alexander
authors.initials: JA
authors.lastname: Cruz Morales
authors.affiliation: Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford OX1 3LB, UK.
authors.forename: Boris
authors.initials: B
authors.lastname: Zilber
keywords: Heisenberg–Weyl algebra; Weyl algebras; Zariski geometries; algebraic Hilbert spaces; quantum mechanics