(adsbygoogle = window.adsbygoogle || []).push({}); Question about this "interaction" in QFT

Hi, I started two months ago my course in QFT, and since I heard about the fact that the bare mass appearing in the Lagrangian of a theory isn't the physical mass of a particle (due to self interaction, I guess), I tried to find an example explicitly solvable where one could see this effect directly. That is find the one particle states of the theory and their energy, E^2= p^2+m^2_physical.

To do so, the simplest model i could think of was the "generalization" of the external current problem presented at the end of the second chapter of Peskin & Schroeder. That is I added to that Lagrangian the free term for the scalar field j(x).

I'm attaching a short .pdf (5 pages) with my calculations and conclusions. The "conclusions section" of my .pdf was a bit rushed, since I hoped that we could discuss it directly on the forum (the very last line, however, seemed very important to me, since it could help to answer some of my other questions i wrote in the .pdf)...

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# Question about this interaction in QFT

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