论文标题
构建附近的通勤矩阵，用于可简化$ su（2）$的可简化表示形式，并向Ogata的定理申请
Constructing Nearby Commuting Matrices for Reducible Representations of $su(2)$ with an Application to Ogata's Theorem
论文作者
论文摘要
解决ARXIV中的Ogata定理的冯·诺伊曼（Von Neumann）的猜想：1111.5933表明，高度非平凡的结果是，任意许多矩阵对应于具有$ n $ sites的宏观可观察物和固定站点尺寸$ d $的宏观可观察结果，在附近是$ n $ n $ n $ n \ tos \ n \ forny \ forny \ forny \ fornty \ fornty \ fornty。在本文中，我们开发了一种构建附近通勤矩阵的方法，用于$ su（2）$的高度还原的表示，其不可约束的亚代表的多样性表现出某种单调减少的行为。然后，我们提供了Ogata定理的站点尺寸$ d = 2 $的建设性证明，并明确估计了附近可观察物的距离。此外，由Arxiv：1012.3494中探索的时间反转对称性的应用激励，我们的构造具有真正的宏观可观察到的属性，即在真正的可观察到的真实通勤的近附近是渐近的。
Resolving a conjecture of von Neumann, Ogata's theorem in arXiv:1111.5933 showed the highly nontrivial result that arbitrarily many matrices corresponding to macroscopic observables with $N$ sites and a fixed site dimension $d$ are asymptotically nearby commuting observables as $N \to \infty$. In this paper, we develop a method to construct nearby commuting matrices for normalized highly reducible representations of $su(2)$ whose multiplicities of irreducible subrepresentations exhibit a certain monotonically decreasing behavior. We then provide a constructive proof of Ogata's theorem for site dimension $d=2$ with explicit estimates for how close the nearby observables are. Moreover, motivated by the application to time-reversal symmetry explored in arXiv:1012.3494, our construction has the property that real macroscopic observables are asymptotically nearby real commuting observables.
