论文标题
Feynman Path积分在紧凑型歧管上的时间切片近似
Time-slicing approximation of Feynman path integrals on compact manifolds
论文作者
论文摘要
我们通过feynman路径积分的时间切片近似，构建了与时间相关的schrödinger方程的基本解决方案。我们表明，短期近似解决方案的迭代将统一操作员拓扑中标量曲率修改的Schrödinger方程的基本解决方案收敛，从SOBOLOLEV空间到方形可集成函数的空间。为了通过我们的方法构造时间布的近似，我们只需要考虑由足够短的经典路径组成的破裂路径。我们通过证明短时近似解决方案的两个重要特性，稳定性和一致性来证明与基本解决方案的收敛性。
We construct fundamental solutions to the time-dependent Schrödinger equations on compact manifolds by the time-slicing approximation of the Feynman path integral. We show that the iteration of short-time approximate solutions converges to the fundamental solutions to the Schrödinger equations modified by the scalar curvature in the uniform operator topology from the Sobolev space to the space of square integrable functions. In order to construct the time-slicing approximation by our method, we only need to consider broken paths consisting of sufficiently short classical paths. We prove the convergence to fundamental solutions by proving two important properties of the short-time approximate solution, the stability and the consistency.
