2012/06/05 by W. G. Brenna, Wilson Brenna, Brenna, Wilson +2
Computer Science · Mathematics · Physics and Astronomy · #Computability, Logic, AI Algorithms #FOS: Mathematics #FOS: Physical sciences #Mathematical and Theoretical Analysis #Operator Algebras (math.OA) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math.OA #quant-ph
paper · pdf · doi:10.48550/arxiv.1206.0809
openalex publication_date 2012/06/05 · arxiv created 2012/10/28 · arxiv updated 2012/10/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Topos theory has been suggested first by Isham and Butterfield, and then by Isham and Doering, 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 recent years the topic has been considerably progressing with the introduction of probabilities, group and group transformations. In the present paper we will introduce a candidate for the complex quantity value object and analyse its relation to the real quantity value object. By defining the Grothendieck k-extension of these two objects, so as to turn them into abelian groups, it is possible to define internal one parameter groups in a topos. We then use this new definition to construct the topos analogue of the Stone's theorem.