DEFORMATION QUANTIZATION: QUANTUM MECHANICS LIVES AND WORKS IN PHASE-SPACE
DEFORMATION QUANTIZATION: QUANTUM MECHANICS LIVES AND WORKS IN PHASE-SPACE
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DOI：
10.1142/s0217751x02006079
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发表时间：
2001-10
影响因子：
1.6
通讯作者：
C. K. Zachos
中科院分区：
文献类型：
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作者：
C. K. Zachos
相空间中的Wigner准概率分布函数是密度矩阵的一种特殊(Weyl)表示。它在描述量子光学中的量子传输、核物理、退相干(例如量子计算)、量子混沌、“Welcher Weg”讨论、半经典极限等方面很有用。它在信号处理中也很重要。然而，由莫亚尔首创的内部逻辑的一个显著方面是在过去的四分之一世纪里才出现的：它提供了量子力学的第三个替代公式，独立于传统的希尔伯特空间或路径积分公式。在这种逻辑上完整和自立的表述中，人们不需要选择边-坐标空间或动量空间。它在全相空间中工作，适应测不准原理。这是对该公式的介绍性概述，并附有简单的插图。
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (e.g. quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a third, alternative, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or Path Integral formulations. In this logically complete and self-standing formulation, one need not choose sides — coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle. This is an introductory overview of the formulation with simple illustrations.