# Transition amplitude for QED+QFD+QCD interactions

As I understood, Feynman diagrams are nothing more than pictures for the transition amplitudes (up to some orders). For this we introduce a interaction vacuum state $$|\Omega\rangle$$ then we are able to calculate: $$\langle\Omega|T\{\phi(x_1)...\phi(x_n)\}|\Omega\rangle$$ I thought this means the creation of some particle at $$x_n$$ and annihilation at some other space time point.

But if I like to have QED/QFD/QCD interactions in one diagram, do I need a common interaction vacuum to write such transition amplitudes (to create for example leptons, W-Bosons or other hadrons in one process)? Is there a common state for QED, QFD and QED or better for the standard model? Or are they different? But how can I interpret these processes in this case?

At the level of perturbation theory, which is commonly used by particle physicists to calculate measurable predictions, the state $\left| \Omega \right>$ (interacting vacuum) can be evaluated assuming the adiabatic hypothesis, which is: interactions are too negligible to influence the states of elementary particles in the far past and future, where the distances between particles were/will be too large for them to interact. An example of the derivation is given in my answer to this PSE question.
Spoiler alert: we account for the change in the vacuum state from $\left| 0 \right>$ to $\left| \Omega \right>$ by excluding the diagrams with disconnected bubble subgraphs (bubble graphs are those which don't have external legs).