上下文统计模型的双曲振幅表示
Representation of the contextual statistical model by hyperbolic amplitudes
摘要：
我们继续开发所谓的上下文统计模型（这里的上下文具有复杂的物理条件的含义）。结果表明，除了上下文产生传统的三角$\cos$ -干扰，存在上下文产生双曲线$\cos$ -干扰。从相应的干扰公式的总概率，我们表示这样的背景下，双曲概率振幅或在抽象的形式主义由正规化向量的双曲模拟的希尔伯特空间。得到了一个双曲玻恩定则。不相容的观测量由非交换算子表示。
英文摘要：
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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