Regularizing Feynman path integrals using the generalized Kontsevich-Vishik trace
Regularizing Feynman path integrals using the generalized Kontsevich-Vishik trace
复制标题
使用广义 Kontsevich-Vishik 迹正则化费曼路径积分
DOI：
10.1063/1.5001147
复制
发表时间：
2017
影响因子：
1.3
通讯作者：
T. Hartung
中科院分区：
文献类型：
--
作者：
T. Hartung
这里给出了费曼路径积分的完全规范的定义。只要路径积分被明确定义，所提出的路径积分的重新表述就与熟悉的表述一致。特别是，它在晶格公式和威克旋转方面是一致的，即它可以用于欧几里得和闵可夫斯基时空。路径积分正则化是通过广义Kontsevich-Vishik迹引入的，即经典迹向傅里叶积分算子的推广。物理上，我们用全纯算子族替换时间演化半群，以便在 C 的某个半空间中很好地定义相应的路径积分。因此，正则化路径积分是通过解析延拓来定义的。这种正则化可以通过稳态相近似来执行，也可以仅根据哈密顿量和可观测值（即先验已知）进行分析计算。在任何一种情况下，评估的计算工作量......
A fully regulated definition of Feynman’s path integral is presented here. The proposed re-formulation of the path integral coincides with the familiar formulation whenever the path integral is well defined. In particular, it is consistent with respect to lattice formulations and Wick rotations, i.e., it can be used in Euclidean and Minkowski space-time. The path integral regularization is introduced through the generalized Kontsevich-Vishik trace, that is, the extension of the classical trace to Fourier integral operators. Physically, we are replacing the time-evolution semi-group by a holomorphic family of operators such that the corresponding path integrals are well defined in some half space of C. The regularized path integral is, thus, defined through analytic continuation. This regularization can be performed by means of stationary phase approximation or computed analytically depending only on the Hamiltonian and the observable (i.e., known a priori). In either case, the computational effort to eval...
DOI：
10.4135/9781483349985.n225
发表时间：
2020
期刊：
The Grants Register 2022
影响因子：
--
作者：
M. Kibuuka
通讯作者：
M. Kibuuka
具有一般泛函的抛物型相空间费曼路径积分
DOI：
--
发表时间：
2022
期刊：
影响因子：
--
作者：
Naoto Kumano-go
通讯作者：
Naoto Kumano-go