The Bargmann-Wigner formalism for spin 2 fields

The Bargmann-Wigner formalism has been applied to describe the spin-2 field in terms of the symmetric fourth-rank multi-Dirac spinor Ψαβγδ. A serious problem of the standard anzatz is that the resulting equation of motion has the trivial solution with all field components being independently equal to zero. We here show that this problem is an artefact of the neglection of terms containing the matrix γ5 in the decomposition of ϕ into the Clifford algebra basis. We further emphasize importance of the gauge 4-vector field in that respect.