An integration by parts formula for Feynman path integrals
An integration by parts formula for Feynman path integrals
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费曼路径积分的分部积分公式
DOI：
10.2969/jmsj/06541273
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发表时间：
2013
影响因子：
0.7
通讯作者：
D. Fujiwara
中科院分区：
文献类型：
--
作者：
D. Fujiwara
本文的目的是提出1。费曼路径积分的时间切片逼近方法综述。2. 适当假设下费曼路径积分的分部积分公式：$\int_{\Omega_{x,y}}DF(\gamma)\lceil p(\gamma)]e^{i\nu S(\gamma)}\mathcal{D}(\gamma)=-\int_{\Omega_{x,y}}F(\gamma)Divp(\gamma)e^{i\nu S(\gamma)}\mathcal{D}(\gamma)$$-iv \int_{\Omega_{x,y}}F(\gamma)DS(\gamma)\lceil p(\gamma)]e^{i\nu S(\gamma)}\mathcal{D}(\gamma)$。这个公式类似于埃尔沃西的维纳积分分部积分公式。Cf . [3]；分部积分公式在$F(\gamma^{*})=$ o情况下的半经典渐近公式中的应用。其中$\gamma^{*}$为相$S(\gamma)$的驻点，即： $\delta S(\gamma^{*})=0.$
The aim of this paper is to present 1. Review of time slicing approximation method of Feynman path integrals introduced by Feynman [4]. 2. An integration by parts formula for Feynman path integrals under suitable assumption: $\int_{\Omega_{x,y}}DF(\gamma)\lceil p(\gamma)]e^{i\nu S(\gamma)}\mathcal{D}(\gamma)=-\int_{\Omega_{x,y}}F(\gamma)Divp(\gamma)e^{i\nu S(\gamma)}\mathcal{D}(\gamma)$ $-iv \int_{\Omega_{x,y}}F(\gamma)DS(\gamma)\lceil p(\gamma)]e^{i\nu S(\gamma)}\mathcal{D}(\gamma)$ . This formula is an analogy to Elworthy’s integration by parts formula for Wiener integrals. cf. [3] 3. An application of integration by parts formula to semiclassical asymptotic formula which holds in the case of $F(\gamma^{*})=$ O. Here $\gamma^{*}$ is the stationary point of the phase $S(\gamma)$ , i.e., $\delta S(\gamma^{*})=0.$