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I know that there are countless threads on virtual particles (some of which I have participated in), but I don't think that this issue has been adressed yet.

One common handwaving argument for the existence of virtual particles is the Heisenberg uncertainty principle. It is said that virtual particles exist shortly enough so that the uncertainty principle applies and lets them "borrow energy from the vacuum".

My question is now: Does this argument have any actual theoretical/mathematical backing within the framework of quantum field theory? Because I don't see how this emerges as a consequence of anything in the theory. Virtual particles emerge as internal lines of Feynman diagrams, it is not clear to me how the uncertainty principle could be related to them.

Let's for now ignore the fact that energy/time uncertainty is a little different from other uncertainties (time does not have a corresponding hermitian operator). Don't let this grow into a "real vs not" discussion, please simply adress my specific question.

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# Energy is borrowed from the vacuum /Virtual Particles

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