Time derivative of creation/annhilation operators

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Discussion Overview

The discussion revolves around the possibility of taking a time derivative of creation and annihilation operators, particularly in the context of quantum field theory (QFT). Participants explore theoretical implications and conditions under which such derivatives might or might not exist.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether it is possible to take a time derivative of creation/annihilation operators.
  • Another participant argues that in QFT, these operators are defined in momentum space and do not depend on position, suggesting that a time derivative may not be applicable.
  • A third participant states that the time derivative of the standard QFT annihilation operator would equal zero, implying a specific case where the derivative is not defined.
  • A fourth participant clarifies that saying the time derivative cannot be taken does not imply that it equals zero, but rather that the derivative does not exist at all.

Areas of Agreement / Disagreement

Participants express differing views on the existence and implications of time derivatives for creation and annihilation operators, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants do not fully explore the mathematical framework or assumptions underlying their claims, leaving some aspects of the discussion open to interpretation.

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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 [itex]\frac{d \hat{a}}{dt}[/itex] 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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