论文标题
在广义不确定性原理中，引力波的共振检测器的路径积分动作
Path integral action for a resonant detector of gravitational waves in the generalized uncertainty principle framework
论文作者
论文摘要
通过引入观察者独立的最小长度来改变海森堡的不确定性原理。在这项工作中，我们考虑了修改的不确定性原理框架中的共振引力检测器，在这种不确定性原理框架中，我们仅将位置动量不确定性关系与二次级校正使用。然后，我们使用路径积分方法在存在引力波的情况下计算棒探测器的动作，然后得出系统的拉格朗日，从而导致在一个维度中构造空间位置坐标的运动方程。然后，我们找到用于检测器坐标的扰动溶液，用于在给定初始条件下，导致相同的经典解。使用检测器的坐标的经典形式，我们最终获得了描述谐波振荡器 - 雷神波系统的壳动作的经典形式。最后，我们获得了包含重力波相互作用的量子波动项的游离粒子传播器。
The Heisenberg uncertainty principle gets modified by the introduction of an observer independent minimal length. In this work we have considered the resonant gravitational wave detector in the modified uncertainty principle framework where we have used the position momentum uncertainty relation with a quadratic order correction only. We have then used the path integral approach to calculate an action for the bar detector in presence of a gravitational wave and then derived the Lagrangian of the system leading to the equation of motion for the configuration-space position coordinate in one dimension. We then find a perturbative solution for the coordinate of the detector for a circularly polarized gravitational wave leading to a classical solution of the same for given initial conditions. Using this classical form of the coordinate of the detector, we finally obtain the classical form of the on-shell action describing the harmonic oscillator-gravitational wave system. Finally, we have obtained the free particle propagator containing the quantum fluctuation term considering gravitational wave interaction.
