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I've a quick a question regarding the make-up of bosonic Green's functions, taking the free propagator for phonons as example. According to Mahan, 3rd ed. it is given by:

D(q, [itex]\lambda[/itex], t-t')=-i[itex]\langle[/itex]0|TA[itex]_{q}[/itex](t)A[itex]_{-q}[/itex](t')|0[itex]\rangle[/itex]

with A[itex]_{q}[/itex]=a[itex]_{q}[/itex]+a[itex]^{+}_{q}[/itex]

[ Eqs. 2.66 & 2.67]

The operators showing up in the propagator ( i.e. A ) are not the simple creation & annihilation operators ( i.e. a, as would be the case for fermions ) but linear combinations thereof. What's the reason for this? Does this imply that phonons are only produced in pairs? Is this the same for other bosonic propagators ( I'm only familiar with phonons ). Hints, Corrections & Solutions greatly appreciated!

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# Structure of the Phonon Free Propagator

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