  The deuteron is considered as a superposition of two-nucleon Fock states with
the invariant mass depending on the relative momentum in a proton-neutron pair.
The condition of the transversality of the polarization vectors should be
imposed at the Fock component level and these vectors depend on the invariant
mass of the Fock component. Such "running" longitudinal polarization vector was
not used in early estimates of relativistic effects. The technique for the
calculation of the average helicity of the proton in the deuteron has been
considered in the light-cone variables. A receipt has been proposed for the
consistent calculation of relativistic nuclear corrections to the average
helicity of the proton in the deuteron and to the first moment of the
spin-dependent structure function of the deuteron.
