The geometric semantics of algebraic quantum mechanics-Reference-Cited by-同舟云学术

The geometric semantics of algebraic quantum mechanics

Published:2015-08-06 Issue:2047 Volume:373 Page:20140245
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Cruz Morales John Alexander¹,Zilber Boris²

Affiliation:

1. Instituto Nacional de Matemática Pura e Aplicada, IMPA, Estrada Dona Castorina 110, Rio de Janeiro 22460-320, Brazil

2. Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK

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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2014.0245

Reference11 articles.

1. Zilber B. 2014 The semantics of the canonical commutation relation . Preprint available at https://people.maths.ox.ac.uk/zilber/sheaf.pdf.

2. Zariski geometries

3. A topos foundation for theories of physics: I. Formal languages for physics

4. Zariski Geometries

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