Category theoretical construction of the figure of states
type: Item
instance of: scholarly article
title: Category theoretical construction of the figure of states
zbMATH Open document ID: 0574.46055
DOI: 10.1007/BF00672653
author: Andrzej Posiewnik
published in: International Journal of Theoretical Physics
publication date: 1985-01-01T00:00:00Z
review text: In this paper we begin to explore the interface or ''junction'' between mathematical description of different physical situations and category theory. We argue that category theory gives a very suitable language to deal with the highly structured situations. The paper provides a construction of the Michnik figure of states of a physical system (the fundamental object in the ''convex'' approach to the foundations of quantum mechanics) according to the rules of category theory. The structure we start with is a compact set of pure states of the system and the construction is represented by the Radon functor. Obtained in such a way the figure of states S is a compact convex set in locally convex Hausdorff topology. The dynamical transformations (operations) are continuous affine maps of the set S into itself.
Mathematics Subject Classification ID: 46M15
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 46E27
Mathematics Subject Classification ID: 28C05
zbMATH DE Number: 3917027
zbMATH Keywords: Michnik figure of states of a physical system
zbMATH Keywords: ''convex'' approach to the foundations of quantum mechanics
zbMATH Keywords: Radon functor
zbMATH Keywords: compact convex set
zbMATH Keywords: continuous affine maps
MaRDI profile type: Publication
cites work: Q5611281
cites work: On the algebraic structure of quantum mechanics
cites work: Q5682456
cites work: Mobility of nonlinear systems
cites work: Q5631608
description: scientific article; zbMATH DE number 3917027