论文标题
关于限制的Feynman路径积分的数学公式通过断线路径
On the mathematical formulation of the restricted Feynman path integrals through broken line paths
论文作者
论文摘要
已提出了受限制的Feynman路径积分（RFPI）来研究物理学的连续量子测量。 RFPI是根据每条路径的通常概率幅度乘以重量的启发性确定的，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，尤其是对于位置测量值，并严格证明这些RFPI在$ l^{2} $空间中得到了很好的定义，并且是对非自我Adjoint Schroedinger方程的解决方案。我们在本文中的结果对Schroedinger方程的通常的Feynman路径积分进行了概括。FurThermore，我们的结果扩展到量子自旋系统。
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.
