arXiv 1302.26162013-02-10quant-phmath-phmath.MP

经典力学、相对论和量子理论基础上的泛函方法

Functional methods underlying classical mechanics, relativity and quantum theory

Alexey A. Kryukov

备注：: IARD 2012 conference talk. Accepted for publication in Journal of Physics
DOI：: 10.1088/1742-6596/437/1/012020

摘要：

本文研究了最近提出的统一了经典力学、相对论和量子理论的标准形式主义的数学框架的物理内容。在这个框架中，经典粒子的态被狄拉克δ函数所识别。经典空间是由这些函数“构成”的，并成为粒子态的希尔伯特空间中的子流形。由此产生的将经典空间嵌入态空间的结果是非常重要的，并解释了经典和量子物理与相对论之间的许多深刻关系。最引人注目的结果之一是证明了宏观粒子位置的正态概率分布（相当于经典空间子流形中相应δ态的位置）产生了任意量子态之间跃迁的玻恩定则。

英文摘要：

The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is "made" of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.

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