论文标题
智障和高级格林的功能满足的数学物理方程
The mathematical physical equations satisfied by retarded and advanced Green's functions
论文作者
论文摘要
在数学物理学中，时间依赖性的绿色功能（GFS）是第一和第二次衍生物的微分方程的解。习惯性地，时间依赖的GF是傅立叶变为频率空间的。然后，将频率的分析延续扩展到实际轴的下方或之上。反傅立叶变换后，可以获得智障和高级GF，并且在这种分析延续中可能存在任意性。在目前的工作中，我们建立了严格解决智障和高级GF的微分方程。关键点是，时间步长函数的导数是dirac delta函数加上无限的数量，其中后者不可忽略，因为它体现了时间延迟或时间推进的含义。本文定义的智障和先进的GF与在多体理论中的创建和破坏操作员的帮助下定义的一体GF相同。在数学物理学中无法定义因果GF，因此给出了原因。这项工作将初始条件放在微分方程中，从而铺平了一种解决问题的方法，即为什么有动作不可逆转。
In mathematical physics, time-dependent Green's functions (GFs) are the solutions of differential equations of the first and second time derivatives. Habitually, the time-dependent GFs are Fourier transformed into the frequency space. Then, analytical continuation of the frequency is extended to below or above the real axis. After inverse Fourier transformation, retarded and advanced GFs can be obtained, and there may be arbitrariness in such analytical continuation. In the present work, we establish the differential equations from which the retarded and advanced GFs are rigorously solved. The key point is that the derivative of the time step function is the Dirac delta function plus an infinitely small quantity, where the latter is not negligible because it embodies the meaning of time delay or time advance. The retarded and advanced GFs defined in this paper are the same as the one-body GFs defined with the help of the creation and destruction operators in many-body theory. There is no way to define the causal GF in mathematical physics, and the reason is given. This work puts the initial conditions into differential equations, thereby paving a way for solving the problem of why there are motions that are irreversible in time.
