Talk:Yukawa interaction

particles?

If two scalar mesons interact through a Yukawa interaction, the potential between the two particles will be:

V(r) = $-{\frac {g^{2}}{4\pi }}{\frac {1}{r}}e^{-m_{\psi }r}$

which is the same as a Coulomb potential except for the sign and the exponential factor.

This looks wrong to me. Shouldn't it be "If two fermions interact through..." ? 160.91.156.238 15:04, 2 October 2007 (UTC)

attactive?

THIS ARTICLE NEEDS REVISION! "Yukawa particle has spin zero and even spin always results in an attractive potential." This statement makes no sense. What about a coulomb bound pionic atom? —Preceding unsigned comment added by 66.45.143.210 (talk) 17:15, 17 November 2008 (UTC)

actually, as far as I know, that statement is correct. I don't see what the bound state you mentioned should entail. Fermions interacting through exchange of a spin-s particle have always attractive potentials if s is even (Yukawa interaction, gravity), and opposite in sign between fermion-fermion and fermion-antifermion if spin is odd (electromagnetism). Proof is in most QFT textbooks, for example Peskin and Schroeder's treatment of the Yukawa interaction, right before the introduction to QED. 95.235.222.104 (talk) 11:27, 8 September 2014 (UTC)

Is this strictly true?

For a (renormalizable) self-interacting field, one will have $V(\phi )={\frac {1}{2}}\mu ^{2}\phi ^{2}+\lambda \phi ^{4}$

Is this the only possibility (even accounting for non-polynomial V)? Might be nice to reference the proof.

afaik, no, you need to assume polynomial V. Non-polynomial Vs might still be renormalizable. There are many reference to this, especially in the theory of the Higgs, maybe I'll be able to find something.95.235.222.104 (talk) 11:27, 8 September 2014 (UTC)

Huh. Right. Interesting. I tweaked the article to add "polynomial". I assume something like the "bootstrap" e.g. like the conformal boostrap might give a non-polynomial term? Or are you thinking something explictly sigma-model-ish or WZW-ish .. ? 67.198.37.16 (talk) 01:07, 5 September 2015 (UTC)

Merge tag. to strong interaction

I'm removing the merge tag. Its been there two years, there's no discussion, no proposal. The strong interaction article is non-technical; this article is highly technical. At any rate, we know that the strong interaction is not just pions, we know that pions are just an approximation. 67.198.37.16 (talk) 01:03, 5 September 2015 (UTC)

Needs to be rewritten for non-experts

This article badly needs to be rewritten to be intelligible for non-experts. Skepticalgiraffe (talk) 17:33, 28 December 2020 (UTC)

Instabilities (2nd paragraph of the classical potential section)

The second paragraph of the classical potential section discusses the exponential term in terms of instabilities and the radioactive decay of the mesons. It should be made clear at the minimum that this radioactive decay has nothing to do with the decaying of real pions -- about 10^-16 seconds for neutral, and 10^-8 seconds for charged. Both of these time-scales are far too long (by orders of magnitude) to notice in the nucleus.

The quantity μ in the exponential is the particle's mass (ħ = c = 1). The potential is the solution of the Klein-Gordon equation with zero time-dependence -- the meson is far off the mass shell. — Preceding unsigned comment added by Johnm307 (talk • contribs) 00:56, 5 February 2021 (UTC)