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I know QED and QCD as isolated theorys but now I thought about particle interactions with QED and QCD processes (like fpr proton-antiproton scattering). But I'm not sure how to interpret this mathematically.

As I understood my Feynman diagrams are nothing more like pictures for the transition amplitueds (up to some orders). For this we introduce a interaction vacuum state [itex]|\Omega\rangle[/itex]. And then we are able to calculate: [tex]\langle\Omega|\phi(x_1)...\phi(x_n)|\Omega\rangle.[/tex] I thougth this means the creation of some particle at [itex]\phi[/itex] at [itex]x_n[/itex] and anihilation at some other space time point.

But if I like to have both interactions in one diagram I need a common interaction vacuum to write such transition amplitueds? Is there a common state for QED and QED or better for the standard model? Or are they different? But how can I interpret these processes in tis case?

Thanks for some answers. Maybe I'm a bit to confused with this whole QFT thing.