Motivated by the recent interest in underground experiments phenomenology (see Refs. 1–3), we review the main aspects of one specific noncommutative space–time model, based on the Groenewold–Moyal plane algebra, the [Formula: see text]-Poincaré space–time. In the [Formula: see text]-Poincaré scenario, the Lorentz co-algebra is deformed introducing a noncommutativity of space–time coordinates. In such a theory, a new quantum field theory in noncommutative space–time can be reformulated. Tackling on several conceptual misunderstanding and technical mistakes in the literature, we will focus on several issues such: (i) the construction of fields theories in [Formula: see text]-Poincaré; (ii) the unitarity of the S-matrix; (iii) the violation of locality, (iv) the violation of the spin-statistic theorem and the Pauli principle; (v) the observables for underground experiments.

中文翻译：

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𝜃-庞加莱的现代指南

受最近对地下实验现象学的兴趣的启发（见参考文献 1-3），我们回顾了一种基于 Groenewold-Moyal 平面代数的特定非对易时空模型的主要方面，即 [公式：见文本]-Poincaré时空。在 [公式：见正文]-Poincaré 场景中，洛伦兹协代数被变形，引入了时空坐标的非交换性。在这样的理论中，可以重新制定非对易时空的新量子场论。针对文献中的几个概念误解和技术错误，我们将重点关注以下几个问题：（i）[公式：见正文]-Poincaré中场论的构建；(ii) S-矩阵的单一性；(iii) 违反局部性，(iv) 违反自旋统计定理和泡利原理；