The geometric semantics of algebraic quantum mechanics

TL;DR

This paper proposes using model theory to provide a geometric semantics for algebraic quantum mechanics, establishing a duality between algebraic and geometric structures to better understand quantum formalism.

Contribution

It introduces a novel approach that employs model theory to connect algebraic and geometric aspects of quantum mechanics, offering new insights into its formalism.

Findings

Establishes a non-commutative duality between algebraic and geometric objects.

Provides a geometric interpretation of quantum formalism.

Lays groundwork for further exploration of quantum mechanics using model theory.

Abstract

In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.