Common structures in scientific theories

Jean Claude Dutailly (1)

1 Chercheur indépendant

The existence of common structures in physics and computer sciences theories has become an active field of research. In the present paper the scope is enlarged, in particular in Economics, to any theory which is formalized in quantitative models meeting some precise but general conditions. The first section is dedicated to characterize the main components of any scientific theory, using the concepts of epistemology, and puts in prominent positions models, association of objects with properties which are represented by quantitative variables. In a second section we show that a large class of models can be represented in Hilbert spaces. In this framework we precise the concepts of observables, with its relation with measures, and develop several tools to characterize the evolution of systems, interacting systems and phases transitions.

Mots clés: system; model; Hilbert; phase; observable; epistemology

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Economies et finances; Econométrie de la finance [q-fin.ST]; Algèbres quantiques [math.QA]

Jean Claude Dutailly. Common structures in scientific theories. 2014. ⟨hal-01003869⟩