标题： 奇点与量子宇宙学中的经典极限 显示英文标题

标题： Singularities and Classical Limit in Quantum Cosmology

摘要： 从Kaluza-Klein理论和低能弦理论导出的极小超空间模型被研究。 它们等价于一个或两个最小耦合的标量场。 获得了普遍的经典和量子解。 构造了WKB解的高斯叠加。 与通常预期的不同，这些状态仅在尺度因子较小的情况下在经典轨迹附近尖锐地集中。 这种行为在因果解释框架中得到证实：许多量子态的Bohm轨迹在尺度因子较小时是经典的，但当尺度因子变大时表现出量子行为。 这一事实的一个后果是这些状态存在初始奇点。 然而，有一些这些波函数的特殊叠加具有无奇点的Bohm轨迹。 也存在一些具有短暂膨胀期的奇异Bohm轨迹，它们永远增长。 我们未能找到任何增长到我们宇宙大小的无奇点轨迹。 显示英文摘要

摘要： Minisuperspace models derived from Kaluza-Klein theories and low energy string theory are studied. They are equivalent to one and two minimally coupled scalar fields. The general classical and quantum solutions are obtained. Gaussian superposition of WKB solutions are constructed. Contrarily to what is usually expected, these states are sharply peaked around the classical trajectories only for small values of the scale factor. This behaviour is confirmed in the framework of the causal interpretation: the Bohmian trajectories of many quantum states are classical for small values of the scale factor but present quantum behaviour when the scale factor becomes large. A consequence of this fact is that these states present an initial singularity. However, there are some particular superpositions of these wave functions which have Bohmian trajectories without singularities. There are also singular Bohmian trajectories with a short period of inflation which grow forever. We could not find any non-singular trajectory which grows to the size of our universe.