Is a non-relativistic approximation possible for the internal dynamics of "elementary" particles?

Abstract

It is pointed out that, contrary to what it is usually implied, the internal dynamics in a compound model of an "elementary" particle is not necessarily relativistic. If the force which binds the constituent objects has a finite range and is not too singular, the relativistic character of the internal motion only depends on the range of such force and on the mass of the constituent particles, not on the depth of the potential well. For instance, for a quark antiquark model of the octet bosons with a quark mass of 5 $GeV$ and a range of the binding force ${(5m_{\mathrm{\pi }})}^{-1}$, one has ${(p/M)}^{\mathit{2}}=\mathit{1}/\mathit{40}$, a non-relativistic situation quite similar to that occurring in nuclei.