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Representation of Contextual Statistical Model by Hyperbolic Amplitudes

Part of the Fundamental Theories of Physics book series (FTPH, volume 160)

Abstract

We continue development of the contextual statistical model—the Växjö model. Besides contexts producing the conventional trigonometric interference, there exist contexts producing the hyperbolic interference. We start with the corresponding formula of total probability with the interference term. Then (in the same way as in the trigonometric case) we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of Hilbert space. A hyperbolic analogue of Born’s rule is obtained. Probabilistically conjugate observables are represented by noncommutative operators.

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Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  1. 1.International Center for Mathematical Modeling in Physics and Cognitive ScienceUniversity of VäxjöVäxjöSweden

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