Representation of the contextual statistical model by hyperbolic amplitudes

Details Representation of the contextual statistical model by hyperbolic amplitudes Representation of the contextual statistical model by hyperbolic amplitudes

2004-08-31

arxiv.org/abs/quant-ph/0408188v2

J. Math. Phys., 46, N.6, 062111 (2005)

Physics

Quantum Physics

We discuss possible applications of hyperbolic quantum mechnaics (in particular, in string theory and cosmology as well as cog

Scientific paper

10.1063/1.1931042

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.

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