论文标题
半经典理论的线性稳定性
Linear stability of semiclassical theories of gravity
论文作者
论文摘要
在玩具模型中研究了半经典理论的线性化理论，该模型由与第二经典标量场相互作用的量子标量场组成，该量子场扮演经典背景的作用。该玩具模型还模仿了半经典爱因斯坦方程引起的进化，例如描述宇宙学情况下早期宇宙的演变。通过构建相应的智障基本解决方案以及讨论相应的初始值问题，可以分析有关该玩具模型简单精确解决方案的线性扰动动力学的方程。结果表明，如果驱动经典背景的后反应的量子场是巨大的，那么有选择的重新归一化参数的选择，在大时的时间内，与紧凑的空间支持的线性扰动在多个时期内均为多个时期，从而表明底层半固有溶液的稳定性。
The linearization of semiclassical theories of gravity is investigated in a toy model, consisting of a quantum scalar field in interaction with a second classical scalar field which plays the role of a classical background. This toy model mimics also the evolution induced by semiclassical Einstein equations, such as the one which describes the early universe in the cosmological case. The equations governing the dynamics of linear perturbations around simple exact solutions of this toy model are analyzed by constructing the corresponding retarded fundamental solutions, and by discussing the corresponding initial value problem. It is shown that, if the quantum field which drives the back-reaction to the classical background is massive, then there are choices of the renormalization parameters for which the linear perturbations with compact spatial support decay polynomially in time for large times, thus indicating stability of the underlying semiclassical solution.
