Group Action in Topos Quantum Physics
arXiv:1110.1650
Abstract
Topos theory has been suggested first by Isham and Butterfield, and then by Isham and Döring, as an alternative mathematical structure within which to formulate physical theories. In particular it has been used to reformulate standard quantum mechanics in such a way that a novel type of logic is used to represent propositions. In this paper we extend this formulation to include the notion of a group and group transformation in such a way that we overcome the problem of twisted presheaves. In order to implement this we need to change the type of topos involved, so as to render the notion of continuity of the group action meaningful.
References in corpus (7)
- A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory
- Abelian subalgebras and the Jordan structure of a von Neumann algebra
- The Gelfand spectrum of a noncommutative C*-algebra: a topos-theoretic approach
- Observables I: Stone Spectra
- A Comparison of Two Topos-Theoretic Approaches to Quantum Theory
- Topos Quantum Logic and Mixed States
- Sheaves in Quantum Topos Induced by Quantization