# (No) Field Renormalization in $\phi^4$ theory at one-loop

What might be the physical intuition behind the fact that we don't need to renormalize the field/wave function at one-loop level in $$\phi^4$$ theory? I justify the field renormalization thinking "the bare field can't connect the vacuum to multi-particle states which are indeed present there due to interaction." Going with this "intuition" I don't see why would we not renormalize the field at one-loop as whenever there is loop there is this possibility of connecting a state with multiparticle states?