论文标题
量子力学的有限变形
Finite Deformations of Quantum Mechanics
论文作者
论文摘要
我们研究了用有限的基团在有限的尺寸希尔伯特空间中替代单一基团的量子力学（QM）的修改，并确定以近似QM的最小序列，以近似QM近似于汉密尔顿的一般选择。这项数学研究揭示了有关“ T Hooft的本体量子力学”以及量子力学统计力学的衍生作用的新见解。我们表明，科尔尼亚克（Kornyak）将QM理解为一个比描述宇宙更高的希尔伯特空间上的经典动力学的建议，并补充了自然保守的量子算子的价值，因为经典的进化可能是我们观察到的世界模型。
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely for general choices of Hamiltonian. This mathematical study reveals novel insights about 't Hooft's Ontological Quantum Mechanics, and the derivation of statistical mechanics from quantum mechanics. We show that Kornyak's proposal to understand QM as classical dynamics on a Hilbert space of one dimension higher than that describing the universe, supplemented by a choice of the value of a naturally conserved quantum operator in that classical evolution can probably be a model of the world we observe.
