Time derivative of creation/annhilation operators

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Basically is it possible to take a time derivative of a creation/annhilation operator?
 
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I think that's not possible. If you are talking about creation and annhilation operators usually found in QFT, they live in the momentum space, so they don't depend on x, but on p. However, I am not sure if in some other circumstances this could be possible.
 
yeah so for eample \frac{d \hat{a}}{dt} would =0 if a was the standard QFT annihilation op
 
Saying you cannot take the "time derivative" does NOT mean that derivative is 0. It means that the derivative does not exist at all.
 

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