Category theoretical construction of the figure of states (Q1063837)

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.