Systems of imprimitivity and representations of quantum mechanics on fuzzy phase spaces
Systems of imprimitivity and representations of quantum mechanics on fuzzy phase spaces
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模糊相空间上的非本原性系统和量子力学表示
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
E. P. ki
中科院分区：
文献类型：
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作者：
S. T. Ali;E. P. ki
根据模糊相空间的一些早期工作，通过与经典力学的类比，将量子力学期望值表示为相空间上非负密度函数的平均值的问题被重新审视。结果表明，如果普通相空间被所谓的模糊相空间取代，那么这种相空间表示是可能的，在模糊相空间上重新定义通常的边缘分布函数以符合位置和动量的任意精确同时测量与量子力学不兼容的事实。在此过程中，获得了关于量子力学相空间表示不存在的维格纳定理的推广，该定理也满足位置和动量的标准（经典）边缘性条件。结果表明，如果位置和动量测量的相应置信函数满足...，则在给定的模糊相空间上存在量子力学的（连续）表示。
The problem of expressing quantum mechanical expectation values as averages with respect to nonnegative density functions on phase space, by analogy with classical mechanics, is reexamined in the light of some earlier work on fuzzy phase spaces. It is shown that such phase space representations are possible if ordinary phase space is replaced by a so‐called fuzzy phase space, on which the usual marginal distribution functions are redefined to conform to the fact that arbitrarily precise simultaneous measurements on position and momentum are not compatible with quantum mechanics. In the process a generalization of Wigner’s theorem on the nonexistence of phase space representations of quantum mechanics, which also satisfy the standard (classical) marginality conditions in position and momentum, is obtained. It is shown that a (continuous) representation of quantum mechanics exists on a given fuzzy phase space if an only if the corresponding confidence functions for position and momentum measurements satisfy...