A Formula of Total Probability with Interference Term and the Hilbert Space Representation of Kolmogorovian Model

 

  • Prof. Andrei Khrennikov – School of Mathematics and Systems Engineering – University of Vaxjo – Sweden
  • FCUL – DEIO – Bloco C/2 – Piso 2 – Sala 2.2.14 – 14:30
  • Quinta-feira, 18 de Setembro de 2003
 
 A Formula of Total Probability with Interference Term and the Hilbert Space Representation of Kolmogorovian Mode

We study generalizations of the formula of total probability for random variables which are sensitive to mutual disturbances induced by measurements. In the conventional probabilistic framework (Kolmogorov, 1933) we derived an analogue of the formula of total probability having an additional additive term -an interference term. In particular, such a formula is used in the standard quantum formalism, where it is derived by using the Hilbert space. However, our investigation is not directly related to quantum theory. We work in the conventional probabilistic formalism. In particular this implies that our interference formula of total probability can be used in various statistical experiments which are not related to quantum theory, e.g., for macroscopic physical systems or cognitive systems.