Homepage     Members     Research     Publications     Gallery    

1. Study of the mathematical structures (algebra, logic, probability, category theory, closure structure, ortho structure, etc...) that are relevant for modern axiomatic quantum mechanics: quantum logics (lattice theory), non-commutative algebra's, non-Kolmogorovian probabilities and the problems that are encountered by the general description of composed systems (existence and construction of co-products in the categories connected to the different mathematical structures).

2. Axiomatics of quantum mechanics (fundamental representation theorem, projective mathematical structures that are related to this, generalized Hilbert spaces, the problem of the field in relation to generalized Hilbert spaces)

3. Foundations of physics, more specifically quantum mechanics and relativity theory, the measurement problem, non-locality and the origin of the space-time structure, the quantum and relativity paradoxes, operational foundations of the mathematical formalisms.

4. The study of the new quantum experiments on individual quantum entities: atom, neutron and photon delocalization and interference experiments. Quantum axiomatics in the light of these new experiments. Description of situation in between quantum and classical and of coupled and separated physical entities. Connections with the Einstein Podolsky Rosen paradox.

5. Quantum computation: the study of computation 'between quantum and classical', the Turing machine as a classical limit of a quantum computer, decoherence and non-locality in the 'between quantum and classical' domain.

Homepage     Members     Research     Publications     Gallery    

Last modified October 27, 2001, by Diederik Aerts