论文标题
重新审视薄壳的量子崩溃
Quantum Collapse of a Thin Shell Revisited
论文作者
论文摘要
对于自我磨损的薄壳的规范描述，有几种可能的选择时间参数，但是构建在不同时间参数上的量子扭动导致单位不相等的描述。我们比较了两个不同时间{\ it viz。，}在壳内部的时间坐标（最初用\ cite {hajicek92a}）和合并观察者（适当时间）的时间坐标。在每种情况下，我们都会为Wheeler-Dewitt方程提供精确的解决方案，仅需要有限且行为良好的$ U（1）$当前。这两种量子理论是互补的，每种理论都强调了普朗克质量的作用：内部时间中正能量的固定状态仅在壳静止质量小于普朗克质量的情况下才存在。在适当的时间内，只有当壳静止质量比planck质量大时，它们才存在。在坐标时间内，既有散射状态和结合状态，均具有明确的能量谱。在适当的时间说明中，只有结合状态，我们确定其频谱。
There are several possible choices of the time parameter for the canonical description of a self-gravitating thin shell, but quantum thories built on different time parameters lead to unitarily inequivalent descriptions. We compare the quantum collapse of a thin dust shell in two different times {\it viz.,} the time coordinate in the interior of the shell (originally addressed in \cite{hajicek92a}) and the time coordinate of the comoving observer (proper time). In each case, we obtain exact solutions to the Wheeler-DeWitt equation requiring only a finite and well behaved $U(1)$ current. The two quantum theories are complementary and each highlights the role played by the Planck mass: stationary states of positive energy in interior time exist only if the shell rest mass in smaller than the Planck mass. In proper time they exist only when the shell rest mass is {\it greater} than the Planck mass. In coordinate time there are both scattering states and bound states with a well defined energy spectrum. In the proper time description there are only bound states, whose spectrum we determine.
