We present a conceptually new formalism for the description of fundamental high-spin states in terms of totally symmetric K-rank Lorentz tensors with Dirac spinor components, $Psi_{\mu_1, ..., \mu_K}$. The formalism employs on equal footing both the mass-shell, and the covariant spin-condition as set by the eigenvalue problem of the operator of the squared Pauli-Lubanski vector. The resulting waveequation is quadratic in the momenta and we couple it minimally to the electromagneticfield . We work out the cases of spin-1 and and spin-3/2 . We find (i) causal propagation of the spin-3/2 field in an electromagneticbackground thus resolving the Velo-Zwanziger problem, and (ii) an universal value of g_s=2 for the gyromagnetic ratio thus invalidating Belinfante's conjecture on the inverse proportionality between gyromagnetic factor and spin.