标题： 从数值量子引力中的持久性幅度 显示英文标题

标题： Persistence Amplitudes from Numerical Quantum Gravity

摘要： 欧几里得量子振幅在初始和最终超曲面上指定的数据之间可能被近似为树振幅 exp(-I_{古典的}/\hbar )，其中 I_{经典的}是连接初始和最终数据的经典解的欧几里得作用量。 在某些情况下，树振幅是精确的。 我们研究 I_{经典的} 从而研究量子振幅，在球对称黎曼引力场与球对称标量场耦合的情况下。 经典标量场服从一个椭圆方程，我们使用松弛技术结合给出引力场的场方程来求解该方程。 给出了从线性到非线性的过渡示例，并展示了作用量的幂律行为。 显示英文摘要

摘要： The Euclidean quantum amplitude to go between data specified on an initial and a final hypersurface may be approximated by the tree amplitude exp(-I_{classical}/\hbar), where I_{classical} is the Euclidean action of the classical solution joining the initial and final data. In certain cases the tree amplitude is exact. We study I_{classical} hence the quantum amplitude, in the case of a spherically symmetric Riemannian gravitational field coupled to a spherically symmetric scalar field. The classical scalar field obeys an elliptic equation, which we solve using relaxation techniques, in conjunction with the field equations giving the gravitational field. An example of the transition from linearity to non-linearity is presented and power law behavior of the action is demonstrated.