  Gamow-Teller(GT) resonances in finite nuclei are studied in a fully
consistent relativistic random phase approximation (RPA) framework. A
relativistic form of the Landau-Migdal contact interaction in the spin-isospin
channel is adopted. This choice ensures that the GT excitation energy in
nuclear matter is correctly reproduced in the non-relativistic limit. The GT
response functions of doubly magic nuclei $^{48}$Ca, $^{90}$Zr and $^{208}$Pb
are calculated using the parameter set NL3 and $g_0'$=0.6 . It is found that
effects related to Dirac sea states account for a reduction of 6-7 % in the GT
sum rule.
