Vacuum expectation values of combinations of ##a^\dagger## and ##a##

[LayMuon]

I am slightly confused on how do we calculate vacuum expectation values of product of creation and annihilation operators for bosons, e.g. $\langle 0| a_{k_1} a^\dagger_{k_2} a_{k_3} a^\dagger_{k_4} |0 \rangle$

If i commute $k_3$ and $k_4$:

$$\langle 0| a_{k_1} a^\dagger_{k_2} a_{k_3} a^\dagger_{k_4} |0 \rangle = \langle 0| a_{k_1} a^\dagger_{k_2} |0 \rangle \delta(k_3-k_4) + \langle 0| a_{k_1} a^\dagger_{k_2} a^\dagger_{k_4} a_{k_3} |0 \rangle $$
Wouldn't the second term give zero automatically because $a |0 \rangle = 0$ ?

 

[strangerep]

Wouldn't the second term give zero automatically because $a |0 \rangle = 0$ ?

Yes.

 

[LayMuon]

thanks.