开放量子系统中具有庞加莱对称性的约化动力学
Reduced dynamics with Poincaré symmetry in an open quantum system
AI总结：
本研究基于庞加莱群幺正表示理论，提出构造开放量子系统中满足庞加莱对称性的动力学映射的系统方法，推导了不同粒子的动力学映射，并证明相关生成元守恒可使无自旋有质量粒子的映射具有幺正性。
摘要：
我们研究了耦合到环境的开放量子系统的约化动力学如何满足庞加莱（Poincaré）对称性。约化动力学由动力学映射描述，该映射通过在无初始关联的情况下从总幺正演化中迹去环境自由度得到。我们研究了在庞加莱群作用下保持不变的动力学映射。基于庞加莱群的幺正表示理论，我们提出了一种构造此类动力学映射的系统方法。利用该方法，我们推导了具有有限自旋的有质量粒子，以及具有有限自旋、非零动量的无质量粒子的动力学映射。我们以无自旋有质量粒子的动力学映射为例，讨论了庞加莱生成元的守恒性。随后，我们找到了同时满足庞加莱不变性和四动量守恒的映射。此外，我们还证明，角动量和 boost 生成元的守恒会使无自旋有质量粒子的映射具有幺正性。
英文摘要：
We consider how the reduced dynamics of an open quantum system coupled to an environment admits the Poincaré symmetry. The reduced dynamics is described by a dynamical map, which is given by tracing out the environment from the total unitary evolution without initial correlations. We investigate the dynamical map which is invariant under the Poincaré group. Based on the unitary representation theory of the Poincaré group, we develop a systematic way to give such a dynamical map. Using this way, we derive the dynamical map of a massive particle with a finite spin and a massless particle with a finite spin and a nonzero momentum. The dynamical map of a spinless massive particle is exemplified and the conservation of the Poincaré generators is discussed. We then find the map with the Poincaré invariance and the four-momentum conservation. Further, we show that the conservation of the angular momentum and the boost operator makes the map of a spinless massive particle unitary
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