We have virtual particles in quantum field theory (QFT). In general, they don't have the need to obey causality.
My question is:
Do the processes in QFT (electron self-energy, photon self-energy, electron-photon vertex, etc.) have to obey causality?
For example, can some parts of the electron self-energy diagram fall out of the light cone?
Or can some parts of the electron-positron annihilation process fall out of the light cone?