标题： 非对易闵可夫斯基时空的热时间 显示英文标题

标题： Thermal time of noncommutative Minkowski spacetime

摘要： 在本文中，我们研究了arXiv:gr-qc/9406019中的热时间假说，在非对易Minkowski变形的背景下。我们表明，动量空间的模函数自然地产生了一个模群。在$\kappa$-Minkowski的具体情况下，我们表明这种热时间流对应于全局定义的时间坐标平移。另一方面，$\rho$-Minkowski缺乏热时间直接与它全局时间的离散性有关。讨论了内自同构变换对物理的影响以及单模情况（非热化时空）的处理方法。此外，提出了对热场理论在量子引力现象学中应用的反思，因为我们刚刚将热时空与$\kappa$-Minkowski联系起来，后者通常被视为一种量子引力候选理论的“平直极限”。 显示英文摘要

摘要： In this paper, we study the thermal time hypothesis of arXiv:gr-qc/9406019 in the context of noncommutative deformations of Minkowski. We show that a natural modular group arises from the modular function of the momentum space. In the specific case of $\kappa$-Minkowski, we show that this thermal time flow corresponds to the globally defined time coordinate translation. On the other hand, the absence of thermal time for $\rho$-Minkowski is directly related to the discreteness of its global time. The impact of inner automorphism transformation on the physics and the treatment of unimodular case (unthermalised spacetimes) are discussed. Moreover, a reflection on the use of thermal field theory for quantum gravity phenomenology is put forward, as we just bridged thermal spacetimes with $\kappa$-Minkowski, often considered a "flat limit" of a quantum gravity candidate theory.