Phase‐space representations of general statistical physical theories
Phase‐space representations of general statistical physical theories
复制标题
一般统计物理理论的相空间表示
DOI：
--
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
W. Stulpe
中科院分区：
文献类型：
--
作者：
M. Singer;W. Stulpe
结果表明，希尔伯特空间量子力学和许多其他统计理论可以在一定的相空间上表示，即状态可以用概率度量来识别，观测值可以用函数来描述。在统计对偶的一般背景下，引入了信息完全可观测，并证明了它们存在的一个定理。指出了这些可观测量与状态到相空间上的概率度量的内射仿射映射之间的对应关系，即相空间表示。特别地，给出了所有可观测的函数的描述，使得在任意好的物理近似下，所有的期望值都可以计算为积分。此外，还讨论了与某些联合位置动量观测有关的量子力学相空间表示的特殊情况的一些新方面。
It is shown that Hilbert‐space quantum mechanics and many other statistical theories can be represented on some phase space, in the sense that states can be identified with probability measures and observables can be described by functions. In the general context of statistical dualities, informationally complete observables are introduced and a theorem on their existence is proven. The correspondence between these observables and the injective affine mappings from the states into the probability measures on phase space, i.e., the phase‐space representations, is pointed out. In particular, a description of all observables by functions is presented, such that all expectation values can, in arbitrarily good physical approximation, be calculated as integrals. Moreover, some new aspects of the particular case of those phase‐space representations of quantum mechanics that are related to certain joint position‐momentum observables are discussed.