Perturbation Expansion for Real‐Time Green's Functions
Perturbation Expansion for Real‐Time Green's Functions
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DOI：
10.1063/1.1664616
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发表时间：
1968-04
影响因子：
1.3
通讯作者：
R. A. Craig
中科院分区：
文献类型：
--
作者：
R. A. Craig
研究了时间平移算子在任意算子的矩阵元中的发展。值得注意的是，我们可以将时间解释为从某个遥远的早期时间（t0）演化到遥远未来的某个时间（t0），然后再回到（t0）。利用这一解释，我们对沿着这条路径定义的绿色函数进行了微扰展开，并将两粒子相互作用项分解为自能项和单粒子绿色函数项，证明了这条路径上的量是合理的。真实的绿色函数和沿着路径定义的绿色函数之间建立了联系，从而得到真实的时间函数的微扰展开式和真实的时间量的运动方程中相互作用项分离的证明。导出了Kadanoff和Baym的输运方程，而不需要从虚时开始进行解析延拓，也不需要Fujita的修正项。
The development of the time‐translation operators in a matrix element of an arbitrary operator is examined. It is noted that we may interpret time as evolving from some remotely early time (t0) to a time in the far future (t∝) and then back to (t0). Using this interpretation, a perturbation expansion is developed for Green's functions defined along this path and a separation of the two‐particle interaction terms into self‐energy parts and single‐particle Green's function terms is justified for quantities on this path. A connection is established between the real‐time Green's functions and the Green's function defined along the path, thereby yielding a perturbation expansion for the real‐time functions and a justification of the separation of the interaction terms in the equations of motion for the real‐time quantities. The transport equations of Kadanoff and Baym are derived without resorting to an analytic continuation from imaginary times and without the correction terms of Fujita.