In the framework of relativistic quantum hadron dynamical theory under
semiclassical, approximation and taking the vacuum fluctuation into a
ccount, a relativistic Vlasov equation (RVE) has been derived. Using R
VE and considering other relativistic effects, we have studied the iso
vector dipole giant resonances built on ground state in spherical nucl
ei. The main results shown that the resonance energies for each multip
ole are larger than those obtained from the non-relativistic classical
Vlasov approach. But by means of choosing a reasonable symmetry poten
tial as 100 MeV, the relativistic results can fit the experimental res
ults very well.