A Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, in m time and n space dimensions, is the group of pseudo-rotations of a pseudo-Euclidean space of signature (m, n). Accordingly, the Lorentz group SO(1, 3) is the common Lorentz transformation group from which special relativity theory stems. It is widely acknowledged that special relativity and quantum theories are at odds. In particular, it is known that entangled particles involve Lorentz symmetry violation. We, therefore, review studies that led to the discovery that the Lorentz group SO(m, n) forms the symmetry group by which a multi-particle system of m entangled n-dimensional particles can be understood in an extended sense of relativistic settings. Consequently, we enrich special relativity by incorporating the Lorentz transformation groups of signature (m, 3) for all m ≥ 2. The resulting enriched special relativity provides the common symmetry group SO(1, 3) of the (1 + 3)-dimensional spacetime of individual particles, along with the symmetry group SO(m, 3) of the (m + 3)-dimensional spacetime of multi-particle systems of m entangled 3-dimensional particles, for all m ≥ 2. A unified parametrization of the Lorentz groups SO(m, n) for all m, n ∈ N, shakes down the underlying matrix algebra into elegant and transparent results. The special case when (m, n) = (1, 3) is supported experimentally by special relativity. It is hoped that this review article will stimulate the search for experimental support when (m, n) = (m, 3) for all m ≥ 2.

中文翻译：

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相对论量子多粒子纠缠的时空对称方法

签名 (m, n), m, n ∈ N 在 m 时间和 n 空间维度上的洛伦兹变换群 SO(m, n) 是签名 (m, n)。因此，洛伦兹群 SO(1, 3) 是狭义相对论起源的常见洛伦兹变换群。众所周知，狭义相对论和量子理论是矛盾的。特别是，已知纠缠粒子涉及洛伦兹对称性破坏。因此，我们回顾了导致发现洛伦兹群 SO(m, n) 形成对称群的研究，通过该对称群，可以在相对论设置的扩展意义上理解 m 纠缠的 n 维粒子的多粒子系统。因此，我们通过结合签名 (m, 3) 对于所有 m ≥ 2。由此产生的丰富的狭义相对论提供了单个粒子的 (1 + 3) 维时空的公共对称群 SO(1, 3)，以及对称群 SO(m, 3) m 纠缠的 3 维粒子的多粒子系统的 (m + 3) 维时空，对于所有 m ≥ 2. 洛伦兹群 SO(m, n) 的统一参数化对于所有 m, n ∈ N，抖动将底层矩阵代数分解为优雅透明的结果。狭义相对论实验支持 (m, n) = (1, 3) 的特殊情况。希望这篇评论文章能在 (m, n) = (m, 3) for all m ≥ 2 时激发对实验支持的搜索。连同 m 纠缠的 3 维粒子的多粒子系统的 (m + 3) 维时空的对称群 SO(m, 3)，对于所有 m ≥ 2. 洛伦兹群 SO(m) 的统一参数化, n) 对于所有 m, n ∈ N，将底层矩阵代数分解为优雅透明的结果。狭义相对论实验支持 (m, n) = (1, 3) 的特殊情况。希望这篇评论文章能在 (m, n) = (m, 3) for all m ≥ 2 时激发对实验支持的搜索。连同 m 纠缠的 3 维粒子的多粒子系统的 (m + 3) 维时空的对称群 SO(m, 3)，对于所有 m ≥ 2. 洛伦兹群 SO(m) 的统一参数化, n) 对于所有 m, n ∈ N，将底层矩阵代数分解为优雅透明的结果。狭义相对论实验支持 (m, n) = (1, 3) 的特殊情况。希望这篇评论文章能在 (m, n) = (m, 3) for all m ≥ 2 时激发对实验支持的搜索。3) 得到狭义相对论的实验支持。希望这篇评论文章能在 (m, n) = (m, 3) for all m ≥ 2 时激发对实验支持的搜索。3) 得到狭义相对论的实验支持。希望这篇评论文章能在 (m, n) = (m, 3) for all m ≥ 2 时激发对实验支持的搜索。