  New solutions of the Bargmann-Wigner equations are obtained: free
fermion-antifermion pairs, each satisfying Dirac's equation, with parallel
momenta and momenta on a plane, produce vectors satisfying Proca's equations.
These equations are consistent with Dirac's and Maxwell's equations, as
zero-order conditions within a Lagrangian expansion for the U(1)-symmetry
quantum field theory. Such vector solutions' demand that they satisfy Maxwell's
equations and quantization fix the charge. The current equates the vector
field, reproducing the superconductivity London equations, thus, binding and
screening conditions. The derived vertex connects to QCD superconductivity and
constrains four-fermion interaction composite models.
