Asymptotic behavior of \(L^2\)-subcritical relativistic Fermi systems in the nonrelativistic limit

We study ground states of a relativistic Fermi system involved with the pseudo-differential operator \(\sqrt{-c^2\Delta +c^4m^2}-c^2m\) $\sqrt{-c^2\mathrm{\Delta }+c^4{m}^2}-c^{2}m$ in the \(L^2\) $L^2$ -subcritical case, where \(m>0\) $m>0$ denotes the rest mass of fermions, and \(c\ge 1\) $c\ge 1$ represents the speed of light. By employing Green’s function and the variational principle of many-fermion systems, we prove the existence of ground states for the system. The asymptotic behavior of ground states for the system is also analyzed in the non-relativistic limit where \(c\rightarrow \infty \) $c\to \infty$ .