Ground states for nonlinear Maxwell–Dirac system with magnetic field

In this paper, we study the following Maxwell–Dirac system with magnetic field and general nonlinearity{∑k=13αk(−i∂k+Ak)u+aβu+ωu−βA0u=Fu(x,u),−ΔA0=4π(βu)u¯=4π|u|2,−ΔAk=4π(αku)u¯,k=1,2,3, for x∈R3x∈R3. Since this problem is strongly indefinite, we use linking and concentration compactness arguments to establish the existence of ground state solutions for this system.