论文标题
宇宙学模型的协变相空间量化
Covariant phase space quantization of cosmological models
论文作者
论文摘要
协变相空间量化试图量化经典解的整个空间，从而导致量子理论缺失了通常的时间坐标。在本文中，我们探讨了该系统量子状态的时间演变如何恢复。我们比较了非派别主义系统（谐波振荡器）和三个相对论量子宇宙学的协方差相空间方法。我们发现，对于非依赖性情况，当一个人在某些表示之间转换时，首选的时间坐标会出现在一个相位因子中，从而使当时间演化运算符在常规量化方法中作用于固定状态时出现的相位。另一方面，对于相对论案例，此阶段因素不再存在，并且似乎恢复了协方差。这些结果与这些模型的其他量化方法一致。
Covariant phase space quantization attempts to quantize the full space of classical solutions, leading to a quantum theory in which the usual time coordinate is missing. In this paper we explore how the time evolution of the quantum states of this system is restored. We compare covariant phase space methods for a nonrelativistic system (the harmonic oscillator) and three relativistic quantum cosmologies. We find that for the nonrelativistic case the preferred time coordinate emerges in a phase factor when one transforms among certain representations, giving exactly the phase that appears when the time evolution operator acts on the stationary states in the usual quantization method. For the relativistic cases, on the other hand, this phase factor is no longer present, and covariance appears to be restored. These results are consistent with other quantization methods for these models.
