I've been learning about Greens functions. I'm familiar with how to find them for different differential operators and situations but far from fully understanding them. We were shown in lecture how they can be used to obtain a perturbation series, leading to Feynman diagrams which represent them. But there was no mention about virtual particles which is what I thought closely related to Feynman diagrams. You include all of the ways a particle and emit, re-absorb and do whatever with the virtual particles and the more events you include the more terms in the series and the more accurate etc.. Do virtual particles arise as a mathematical consequence of Greens function then, and if so how? Thanks in advance!