Elaboration of a new topological framework for a generalized quantum mechanics.

Project Details

Description

Several years ago, one of the promotors of this project proved several results showing that when a property of a fysical system is represented by a set of states actualising the property, a natural closure structure arises on the set of properties. The lattice structure, one usually works with, then appears as the set of closed subsets for the closure structure. The purpose of the project is to investigate the category of closure spaces. In this study we will be guided by methods from categorical topology on one hand and by the fysical laws on the other hand. In this respect the participation of the different research groups involved in the project is essential. The composition of the group guarantees the interdiscipinary character of the research. We will investigate whether certain topological notions in the mathematical model of closure spaces also have a fysical meaning. In particular we have in mind the investigation of certain separation properties. Categorical topology offers the general methods to introduce these topological properties. Our belief that these properties may be linked to the fysical context is motivated by earlier results of one of the promotors regarding the fysical interpretation of the Ta and T1 topological separation axioms.
AcronymOZR16
StatusFinished
Effective start/end date1/01/9731/12/00

Flemish discipline codes

  • Mathematical sciences

Keywords

  • mathematics
  • science