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

1. May 23, 2013

### 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 $a |0 \rangle = 0$ ?

2. May 23, 2013

### strangerep

Yes.

3. May 23, 2013

thanks.