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In this paper, we investigate the nonrelativistic limit of normalizedsolutions to a nonlinear Dirac equation as given below: \begin{equation*}  \begin{cases} &-i c\sum\limits_{k=1}^3\alpha_k\partial_k u +mc^2 \beta {u}-\Gamma * (K |{u}|^\kappa) K|{u}|^{\kappa-2}{u}- P |{u}|^{s-2}{u}=\omega {u}, \\&\displaystyle\int_{\mathbb{R}^3}\vert u \vert^2 dx =1.  \end{cases} \end{equation*} Here, $c>0$ represents the speed of light, $m >0$ is the mass of the Dirac particle, $\omega\in\mathbb{R}$ emerges as anindeterminate Lagrange multiplier, $\Gamma$, $K$, $P$ are real-valued functiondefined on $\mathbb{R}^3$, also known as potential functions. Our researchfirst confirms the presence of normalized solutions to the Dirac equation underhigh-speed light conditions. We then illustrate that these solutions progressto become the ground states of a system of nonlinear Schr\"odinger equationswith a normalized constraint, exhibiting uniform boundedness and exponentialdecay irrespective of the light speed. Our results form the first discussion onnonrelativistic limit of normalized solutions to nonlinear Dirac equations.This not only aids in the study of normalized solutions of the nonlinearSchr\"odinger equations, but also physically explains that the normalizedground states of high-speed particles and low-speed motion particles areconsistent.

Nonrelativistic Limit of Normalized Solutions to a class of nonlinear Dirac equations