Usually when one speaks of effective field theories, one is looking to integrate out certain fields which are typically heavy in comparison to the regime of interest. That is one has a theory at a high energy and obtains/writes down a matching theory where this heavy degrees of freedom have been averaged out.

Are there any notions in the community of the inverse procedure. I am looking for some procedure along the lines: Start with a theory you believe explains a wide of regimes of energies and focus on the higher energy cases by "integrating out" degrees of freedom which one expects will only contribute too little at those scales, thus obtaining an effective description for the high energy section.

  • $\begingroup$ No one does this, for the fairly obvious reason that the low energy modes are most important, will contribute importantly at high energies, and a theory without them would be drastically nonlocal. The reason for that is, when you integrate out modes up to some energy scale $\Delta$, you introduce nonlocality on a scale $1/\Delta$ (interactings involving exchange of modes at scale $\Delta$ are ignored so it looks like you have action at a distance of $1/\Delta$). So if you integrate out degrees of freedom $\Delta \approx 0$ then your theory is very nonlocal and nonunitary $\endgroup$ – user213887 Dec 10 '18 at 16:53
  • $\begingroup$ Sure I understand the energy scale itself won't be a "proper" expansion parameter for such procedure, but perhaps some other method allows one to detach the low energy physics, analogous to a lower momentum cut-off to deal with infrared divergences. I am also sceptical about the idea on its own but seemed worth asking around... $\endgroup$ – ohneVal Dec 10 '18 at 16:56
  • $\begingroup$ Every monograph I've ever read on EFT is pretty adamant it's only low energy physics we care about so I'm 99% sure no one is interested. A high energy particle can emit infinitely many soft modes - that's the most important physics to parametrise. I mean, what other excitations would you want to keep track of? Those with energies greater than the scale of your experiment? Clearly those won't contribute as much, because you don't have enough energy to excite them! $\endgroup$ – user213887 Dec 10 '18 at 17:02
  • $\begingroup$ Well not necessarily out of my experiment, on the contrary, I was thinking more like ignoring the physics happening let's say below the sensitivity of my detector, something of that sort. Then again, thank you for your input Julian. $\endgroup$ – ohneVal Dec 10 '18 at 17:43
  • $\begingroup$ Oh! Okay - what you're talking about sounds similar to the way of dealing with IR divergences/jets, idk if you're familiar with this story? $\endgroup$ – user213887 Dec 10 '18 at 17:57

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