Topos theory and `neo-realist' quantum theory
arXiv:0712.4003 · doi:10.1007/978-3-7643-8736-5_2
Abstract
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, emphasising 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.
22 pages, no figures; contribution for Proceedings of workshop "Recent Developments in Quantum Field Theory", MPI MIS Leipzig, July 2007
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- Problem of Time in Quantum Gravity
- Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme
- Quantum States and Measures on the Spectral Presheaf
- Self-adjoint Operators as Functions II: Quantum Probability
- Quantum Exotic PDE's
- Topos Quantum Logic and Mixed States
- Topos Analogues of the KMS State
- A Topos Formulation of Consistent Histories
- Group Action in Topos Quantum Physics
- Lectures on Topos Quantum Theory