Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1004.3564

Topos Methods in the Foundations of Physics

Chris Isham

Published Apr 20, 2010• 0 citations
arXivHTMLPDF

Abstract

This article gives a conceptual introduction to the topos approach to the formulation of physical theories.
DOI
10.48550/arxiv.1004.3564

Related papers

“What is a Thing?”: Topos Theory in the Foundations of Physics

A. Döring, C. Isham

arXiv:0803.0417•Lecture notes in physics•Jan 1, 2010•127 citations

Lectures on Topos Quantum Theory

Cecilia Flori

This is a series of lecture notes explaining topos theory and its application in physics.

arXiv:1207.1744•Jul 6, 2012•3 citations

Brief Introduction to Covariant Topos Quantum Theory

Cecilia Flori

Lecture notes in physics•Jan 1, 2018•0 citations

Topos formulation of History Quantum Theory

Cecilia Flori

Bulletin of the American Physical Society•Mar 22, 2011•0 citations

The Physical Interpretation of Daseinisation

Andreas Döring

Introduction This chapter provides a conceptual discussion and physical interpretation of some of the quite abstract constructions in the topos approach to physics. In particular, the daseinisation process for projection operators and for self-adjoint operators is motivated and explained from a physical point of view. Daseinisation provides the bridge between the standard Hilbert space formalism of quantum theory and the new topos-based approach to quantum theory. As an illustration, I show all constructions explicitly for a three-dimensional Hilbert space and the spin- z operator of a spin-1 particle. Throughout, I refer to joint work with Chris Isham, and this chapter is intended to serve as a companion to the one he contributed to this volume. The Topos Approach The topos approach to quantum theory was initiated by Isham [21] and Butterfield and Isham [19, 22–24]. It was developed and broadened into an approach to the formulation of physical theories in general by Isham and by this author [12–15]. The long article [16] gives a more or less exhaustive and coherent overview of the approach. More recent developments are the description of arbitrary states by probability measures [9] and further developments [10] concerning the new form of quantum logic that constitutes a central part of the topos approach. For background, motivation, and the main ideas, see also Isham's Chapter 3 in this volume.

Cambridge University Press eBooks•Apr 18, 2011•30 citations

Topos Theory and ‘Neo-Realist’ Quantum Theory

Andreas Döring

Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasizing the logical aspects. Each topos serves as a ‘mathematical universe’ with an internal logic, which is used to assign truth-values to all propositions about a physical system. We show in detail how this works for (algebraic) quantum theory.

arXiv:0712.4003•Birkhäuser Basel eBooks•Jan 1, 2009•29 citations
Introduction This chapter provides a conceptual discussion and physical interpretation of some of the quite abstract constructions in the topos approach to physics. In particular, the daseinisation process for projection operators and for self-adjoint operators is motivated and explained from a physical point of view. Daseinisation provides the bridge between the standard Hilbert space formalism of quantum theory and the new topos-based approach to quantum theory. As an illustration, I show all constructions explicitly for a three-dimensional Hilbert space and the spin- z operator of a spin-1 particle. Throughout, I refer to joint work with Chris Isham, and this chapter is intended to serve as a companion to the one he contributed to this volume. The Topos Approach The topos approach to quantum theory was initiated by Isham [21] and Butterfield and Isham [19, 22–24]. It was developed and broadened into an approach to the formulation of physical theories in general by Isham and by this author [12–15]. The long article [16] gives a more or less exhaustive and coherent overview of the approach. More recent developments are the description of arbitrary states by probability measures [9] and further developments [10] concerning the new form of quantum logic that constitutes a central part of the topos approach. For background, motivation, and the main ideas, see also Isham's Chapter 3 in this volume.