论文标题
Feynman图在壳传播器方面
Feynman diagrams in terms of on-shell propagators
论文作者
论文摘要
结果表明，Feynman图的通常表达方式是Feynman繁殖者$Δ_F（X-Y）$的表达，可以用等效表达式代替涉及正能量的固定传播剂$Δ^+（X-Y）$，并补充了与时间顺序相关的适当功能。当这种表达Feynman图的这种替代方法是将傅立叶转换为动量空间时，与每个函数相关的动量$δ^+（x-y）$是壳上的，并且只有在能量归因于时间顺序函数的贡献时，只有在每个顶点保守。最终的表达方式类似于Kadyshevsky通过得出$ s $ - 矩阵的替代扩展而获得的。关于如何得出这种替代扩展的详细说明，并显示了它如何提供一种直接的方法来确定Feynman图的虚构部分，这使得在使用Unitarity方法计算Feynman图时，它使其有用。通过考虑自我相互作用标量模型中的许多特定的Feynman图，并在QED中，我们展示了这种替代方法如何与旧的扰动理论相关，并可以简化Feynman图的直接计算。
It is shown that the usual expression for a Feynman diagram in terms of the Feynman propagator $Δ_F(x-y)$ can be replaced by an equivalent expression involving the positive-energy on-shell propagator $Δ^+(x-y)$, supplemented by appropriate functions associated with time-ordering. When this alternate way of expressing a Feynman diagram is Fourier transformed into momentum space, the momentum associated with each function $Δ^+(x-y)$ is on-shell, and is only conserved at each vertex if an energy is attributed to the contributions of the time-ordering functions. The resulting expression is analogous to what Kadyshevsky had obtained by deriving an alternate expansion for the $S$--matrix. A detailed explanation of how this alternate expansion is derived is given, and it is shown how it provides a straightforward way of determining the imaginary part of a Feynman diagram, which makes it useful when using unitarity methods for computing a Feynman diagram. By considering a number of specific Feynman diagrams in self-interacting scalar models and in QED, we show how this alternate approach can be related to the old perturbation theory and can simplify direct calculations of Feynman diagrams.
