Many-particle relativistic equations for fermions

Many-particle equations for fermions are investigated in the framework of Lagrangian field theory by using a Legendre transformation of the generating functional of the Green's functions. The general form of the $n$-fermion equation is established and the connected structure of the kernel is investigated. For the trilinear interaction $\overline\psi\mathscr{O}\psi{A}$ a relationship is obtained between the kernel of the $n$-particle equation and the $(2n+1)$-point Green's function.