Normalized solutions for Sobolev critical Schrödinger-Bopp-Podolsky systems

We study the Sobolev critical Schrödinger-Bopp-Podolsky system \begin{gather*} -Δu+φu=λu+μ|u|^{p-2}u+|u|^4u\quad $\text{in }$$\mathbb{R}$^3, -Δφ+Δ^2φ=4πu^2\quad $\text{in }$ $\mathbb{R}$^3, \end{gather*} under the mass constraint $${\int }_{{\mathbb{R}}^3}{u}^{2}dx=c$$ for some prescribed $c>0$, where $2<p<8\mathrm{/}3$, $\mu >0$ is a parameter, and $\lambda \in \mathbb{R}$ is a Lagrange multiplier. By developing a constraint minimizing approach, we show that the above system admits a local minimizer. Furthermore, we establish the existence of normalized ground state solutions.