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Short introduction to my understanding: As far as i understand, virtual particles are usually defined to be the internal lines in Feynman Diagrams. But we know that those are just useful tools to calculate amplitudes in interacting quantum field theories. In a free theory I have no interactions, hence no internal lines and no virtual particles. Virtual particles show up when, in interacting QFTs, we have the so called contact interactions showing up in the perturbative Dyson-Schwinger equations as deltas.

My question:

Can we regard virtual particles solely as mathematical tools needed to make predictions in perturbative interacting theories because we don't fully understand how interacting theories work? (I mean how they work in a non-perturbative setting)

If the latter is true, and from my actual understanding I think it is true, what is our "hole" in the understanding of full interacting QFTs?

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    $\begingroup$ It's better to ask which things are not holes. $\endgroup$
    – Connor Behan
    May 3 at 0:08
  • $\begingroup$ This Phys.SE thread may answer you what's the issue with interactions in QFT: physics.stackexchange.com/q/330536 $\endgroup$
    – Gold
    May 3 at 0:09
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    $\begingroup$ Yes, virtual particles are just tools. This has been discussed in many questions here. The hole is that it's not that easy to exactly solve a non-Gaussian integral. $\endgroup$
    – Avantgarde
    May 3 at 0:28
  • $\begingroup$ Nice pun @ConnorBehan. $\endgroup$
    – LolloBoldo
    May 3 at 0:50
  • $\begingroup$ Thanks for the link, i'll take a look. I know that non-gaussian integrals are kinda bad, i was wondering if there is more to it than just nasty integrals $\endgroup$
    – LolloBoldo
    May 3 at 0:51

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