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首页> 外文期刊>Journal of High Energy Physics, Gravitation and Cosmology >Observables and Dynamics Quantum to Classical from a Relativity Symmetry and Noncommutative-Geometric Perspective
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Observables and Dynamics Quantum to Classical from a Relativity Symmetry and Noncommutative-Geometric Perspective

机译：相对论对称性和非交换几何学视角下的可观量和动力学量子到经典

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With approaching quantumoncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate here the WWGM formalism starting from the canonical coherent states and taking wavefunctions as expansion coefficients in terms of this basis. This provides us with a transparent and coherent story of simple quantum dynamics where both the wavefunctions for the pure states and operators acting on them arise from the single space/algebra , which exactly includes the WWGM observable algebra. Altogether, putting the emphasis on building our theory out of the underlying relativity symmetry—the centrally extended Galilean symmetry in the case at hand—allows one to naturally derive both a kinematical and a dynamical description of a quantum particle, which moreover recovers the corresponding classical picture (understood in terms of the Koopman-von Neumann formalism) in the appropriate (relativity symmetry contraction) limit. Our formulation here is the most natural framework directly connecting all of the relevant mathematical notions and we hope it may help a general physicist better visualize and appreciate the noncommutative-geometric perspective behind quantum physics. It also helps to inspire and illustrate our perspective on looking at quantum mechanics and quantum physics in general in direct connection to the notion of quantum (deformed) relativity symmetries and the corresponding quantumoncommutative models of spacetime as various levels of approximations all the way down to the Newtonian.
机译：考虑到针对深空微观时空的接近量子/非交换模型，并受到我们最近对（射影）希尔伯特空间作为基本量子力学背后物理空间模型的描述的启发，我们在此处重新表述了从规范相干态开始的WWGM形式主义以此为基础，将波函数作为展开系数。这为我们提供了一个简单而透明的，简单的量子动力学故事，其中纯态的波函数和作用于它们的算符均来自单个空间/代数，其中恰好包括WWGM可观代数。总而言之，将重点放在基于相对论对称性的基础上建立我们的理论（在本例中为中心扩展的伽利略对称性），使人们可以自然地得出量子粒子的运动学和动力学描述，而且还可以恢复相应的经典图片（用考夫曼-冯·诺伊曼形式主义理解）处于适当的（相对论对称收缩）极限。我们在这里的表述是最直接联系所有相关数学概念的最自然的框架，我们希望它可以帮助普通物理学家更好地可视化和欣赏量子物理学背后的非可交换几何观点。它也有助于激发和说明我们与量子（变形）相对论对称性概念以及相应的时空量子/非交换模型直接相关的概念，即从各个层面上一直向下近似的量子力学和量子物理学的观点。到牛顿。

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