%0 Journal Article
%T Representation of the contextual statistical model by hyperbolic amplitudes
%A A. Yu. Khrennikov
%J Mathematics
%D 2004
%I arXiv
%R 10.1063/1.1931042
%X We continue the development of a so called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric $\cos$-interference, there exist contexts producing the hyperbolic $\cos$-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators.
%U http://arxiv.org/abs/quant-ph/0408188v2