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Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 3, Pages 518–536
DOI: https://doi.org/10.4213/tvp37
(Mi tvp37)
 

This article is cited in 10 scientific papers (total in 10 papers)

A formula of total probability with interference term and the Hilbert space representation of the contextual Kolmogorov model

A. Yu. Khrennikov

Växjö University
References:
Abstract: 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.
Received: 30.04.2004
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 3, Pages 427–441
DOI: https://doi.org/10.1137/S0040585X97982505
Bibliographic databases:
Language: Russian
Citation: A. Yu. Khrennikov, “A formula of total probability with interference term and the Hilbert space representation of the contextual Kolmogorov model”, Teor. Veroyatnost. i Primenen., 51:3 (2006), 518–536; Theory Probab. Appl., 51:3 (2007), 427–441
Citation in format AMSBIB
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\paper A formula of total probability with interference term and the Hilbert space representation of the contextual Kolmogorov model
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\pages 518--536
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\transl
\jour Theory Probab. Appl.
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\pages 427--441
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  • https://www.mathnet.ru/eng/tvp37
  • https://doi.org/10.4213/tvp37
  • https://www.mathnet.ru/eng/tvp/v51/i3/p518
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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