# Causality and processes in QFT

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?

No, to my knowledge causality is a crucial part of quantum field theory. Everything that can be measured has to obey causality. For bosons, this corresponds to the fact that $$\langle 0|[\phi(x), \phi^*(y)]|0 \rangle$$ is always zero at space-like separation. For fermions, we know that $$\langle 0| \lbrace \psi(x), \bar{\psi}(y) \rbrace |0 \rangle$$ is zero outside the light cone. Since operators such as charge, energy, and momentum always involve an even number of spinor fields, this is enough to ensure that $$[\mathcal{O}_1(x), \mathcal{O}_2(y)]$$ is also zero outside the light-cone. Which says no two measurements can effect each other at space-like separation.