关于通过折线路径的限制Feynman路径积分的数学表述
On the mathematical formulation of the restricted Feynman path integrals through broken line paths
摘要：
限制费曼路径积分（RFPI）是研究物理学中连续量子测量的一种新方法。RFPI是根据通常的概率幅度乘以每条路径的权重来确定的，其中包含有关测量设备的结果和分辨率的信息。在本文中，我们将考虑RFPI特别是位置测量，并严格证明，这些RFPI是很好地定义在$L^{2}$空间和非自伴薛定谔方程的解决方案。本文的结果推广了薛定谔方程通常的Feynman路径积分的结果，并将其推广到量子自旋系统.
英文摘要：
The restricted Feynman path integrals (RFPIs) have been proposed to study continuous quantum measurements in physics. The RFPIs are heuristically determined in terms of the usual probability amplitude multiplied by weight for each path, which contains information about the results and the resolution of the measuring device. In the present paper we will consider the RFPIs particularly for the position measurements and will prove rigorously that these RFPIs are well defined in the $L^{2}$ space and are the solutions to the non-self-adjoint Schroedinger equations. Our results in the present paper give a generalization of the results on the usual Feynman path integrals for the Schroedinger equations.Furthermore, our results are extended to quantum spin systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
