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##(adsbygoogle = window.adsbygoogle || []).push({});

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## ?

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

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