薛定谔时空几何、整体坐标与谐波捕获
Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping
摘要：
我们研究了动力学指数z>1的Schroedinger时空的各种几何性质，并与AdS（z=1）的性质进行了比较。薛定谔度量对于1<z<2是奇异的，而通常的庞加莱坐标对于z \geq 2是不完整的。对于z=2，我们得到了一个全球坐标系，我们解释了它的测地完备性，全球时间的选择，和非相对论CFTs的谐波捕获之间的关系。当z>2时，我们证明了薛定谔时空不存在整体类时Killing向量。
英文摘要：
We study various geometrical aspects of Schroedinger space-times with dynamical exponent z>1 and compare them with the properties of AdS (z=1). The Schroedinger metrics are singular for 1<z<2 while the usual Poincare coordinates are incomplete for z \geq 2. For z=2 we obtain a global coordinate system and we explain the relations among its geodesic completeness, the choice of global time, and the harmonic trapping of non-relativistic CFTs. For z>2, we show that the Schroedinger space-times admit no global timelike Killing vectors.
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