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There is a 'folk theorem' I've encountered that goes something like this: trying to localize a relativistic particle indefinitely will result in the creation of other particles. This is sometimes taken as the physical explanation for the non-existence of relativistic position operators. (The eigenvectors of the Newton-Wigner operators are unphysical since they spread to the entire Universe in a finite time interval.) Can someone please give me references where such things are proved or at least made precise?

Gerald Kaiser
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    It's not a "folk theorem" but a fairly trivial consequence of the fact that "localization of a field" takes energy. The "particle creation" aspect is, of course, primarily a misunderstanding. There are no quanta in the free field. But since we are raising the energy density of the field by boxing it in, we can get that energy back out, which has to happen by a quantized absorption process. This also means that the "boxing in" process itself has to be quantized. – FlatterMann Oct 23 '22 at 01:33
  • Thanks, but I'm interested in localizing a relativistic particle, not the entire field. I would be happy with a derivation of the minimum energy required to do so, however the latter is defined. – Gerald Kaiser Oct 23 '22 at 21:19
  • Related: https://physics.stackexchange.com/q/98711/36793 – SRS Oct 24 '22 at 08:07

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