The spontaneously broken supersymmetry in quantum field theory

It is shown that every spontaneous breaking of supersymmetry can be accomplished by means of a locally conserved supercurrent

$\text{εαβf}{}^{\mathrm{+}}{}_{\mathrm{<mtext>\gamma </mtext><mtext>?</mtext>}}\text{, α, β, γ = 1, 2,}$

$\text{εαβ =}\text{0}\text{1}\text{?1}\text{1}$

, where $\text{f}{}^{\mathrm{+}}{}_{\mathrm{<mtext>\gamma </mtext><mtext>?</mtext>}}$ is a massless field satisfying the Weyl Equation. For a given supercurrent $\text{jαβ}\text{γ}\text{?}$ the necessary condition that it will break spontaneously the supersymmetry is

$\text{jαβ}\text{γ}\text{?}\text{?jβα}\text{γ}\text{?}\text{≠0.}$

It is shown that the anticommutation relations of the broken supercharges are not related to the energy-momentum vector.Similar procedure applied in case of a vector field is inconclusive.The extension of the Maisson and Reeh statement on the helicity of Goldstone fields is given.