Phase space Feynman path integrals of higher order parabolic type with general functional as integrand
Phase space Feynman path integrals of higher order parabolic type with general functional as integrand
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DOI：
10.1016/j.bulsci.2014.11.001
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发表时间：
2015-07
影响因子：
1.3
通讯作者：
Naoto Kumano-go;A. Murthy
中科院分区：
文献类型：
--
作者：
Naoto Kumano-go;A. Murthy
本文给出了一类泛函，对于这类泛函，高阶抛物型的相空间费曼路径积分具有严格的数学意义。更确切地说，对于属于我们类的任何泛函，相空间路径积分的时间切片近似相对于位置路径的端点和动量路径的起点均匀收敛于紧致子集上。我们的泛函类是丰富的，因为它对加法和乘法是封闭的。阶与时间积分的交换、阶与极限的交换和微扰展开公式在路径积分中成立。
We give a general class of functionals for which the phase space Feynman path integrals of higher order parabolic type have a mathematically rigorous meaning. More precisely, for any functional belonging to our class, the time slicing approximation of the phase space path integral converges uniformly on compact subsets with respect to the endpoint of position paths and to the starting point of momentum paths. Our class of functionals is rich because it is closed under addition and multiplication. The interchange of the order with the integration with respect to time, the interchange of the order with a limit and the perturbation expansion formula hold in the path integrals.