Geodesic
A formula of total probability with interference term and the Hilbert space representation of the contextual Kolmogorov model
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 518-536

Voir la notice de l'article provenant de la source Math-Net.Ru

We compare the classical Kolmogorov and quantum probability models. We show that the gap between these models is not so huge as was commonly believed. The main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the Kolmogorov model. In particular, we obtain “interference of probabilities” without appealing to the Hilbert space formalism. We interpret “interference of probabilities” as a perturbation (by a cos-term) of the conventional formula of total probability. Our classical derivation of quantum probabilistic formalism can stimulate applications of quantum methods outside of the microworld, for instance, in psychology, biology, economy, and other domains of science.
Keywords: formula of total probability, contextual Kolmogorov model, quantum representation, interference of probabilities, Born's rule. 
@article{TVP_2006_51_3_a4,
     author = {A. Yu. Khrennikov},
     title = {A formula of total probability with interference term and the {Hilbert} space representation of the contextual {Kolmogorov} model},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {518--536},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a4/}
}
TY  - JOUR
AU  - A. Yu. Khrennikov
TI  - A formula of total probability with interference term and the Hilbert space representation of the contextual Kolmogorov model
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2006
SP  - 518
EP  - 536
VL  - 51
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a4/
LA  - ru
ID  - TVP_2006_51_3_a4
ER  - 
%0 Journal Article
%A A. Yu. Khrennikov
%T A formula of total probability with interference term and the Hilbert space representation of the contextual Kolmogorov model
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2006
%P 518-536
%V 51
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a4/
%G ru
%F TVP_2006_51_3_a4
A. Yu. Khrennikov. A formula of total probability with interference term and the Hilbert space representation of the contextual Kolmogorov model. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 518-536. http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a4/