论文标题
多时间积分方程的概率保护
Probability conservation for multi-time integral equations
论文作者
论文摘要
在相对论量子理论中，有时会考虑波函数$ψ（x_1，x_2）$的积分方程，具体取决于两个粒子的两个时空点。这种方程式的一个严重问题是，通常，$ |ψ|^2 $上的空间积分在及时并不保守 - 这与量子理论的基本概率解释相抵触。但是，这里表明，对于具有延迟相互作用沿光锥的智障相互作用的特殊类别的方程式，实际上，全球概率积分在所有cauchy表面上都是保守的。对于另一类具有更通用的相互作用内核的积分方程，从$ t = - \ infty $到$ t =+\ infty $的渐近概率保存显示为真实。此外，从第一个结果推论了某些地方保护法。
In relativistic quantum theory, one sometimes considers integral equations for a wave function $ψ(x_1,x_2)$ depending on two space-time points for two particles. A serious issue with such equations is that, typically, the spatial integral over $|ψ|^2$ is not conserved in time -- which conflicts with the basic probabilistic interpretation of quantum theory. However, here it is shown that for a special class of integral equations with retarded interactions along light cones, the global probability integral is, indeed, conserved on all Cauchy surfaces. For another class of integral equations with more general interaction kernels, asymptotic probability conservation from $t=-\infty$ to $t=+\infty$ is shown to hold true. Moreover, a certain local conservation law is deduced from the first result.
