Local interactions of higher-spin potentials that are gauge invariant in linear approximation

We study connected Wightman functions of N conserved currents, each of which is formed from a scalar field and has even spin l _i . The UV divergence of this vertex function is regularized by the analytic continuation in the space dimension D → D − ε. We evaluate the residue of ε ⁻¹ only, which is a local interaction Lagrangian density and gauge invariant in linear approximation. The text was submitted by the author in English.