A question about Wick theorem?

[ndung200790]

I think that Wick theorem permits us to contract boson field operator with fermion field operator(?).Because the commutator between fermion and boson field operators is like commutator between two boson field operators.Then why in Feynman diagrams do we only consider propagators of boson,fermion and ghost fields separately,but do not consider ''complex'' propagator of boson and fermion fields?.Is this because the conservation of of particle types.If it is,how can we deduce the conservation law from QFT?

 

[ndung200790]

Sorry,now I have found the question:the commutator between boson and fermion field operators is simply zero,so that the corresponding propagator is zero.