Stability of relativistic Hartree states

It is shown that the Hartree solution of a relativistic hamiltonian of the type considered by Walecka and collaborators is unstable with respect to particle-hole excitations responsible for fluctuations of the nucleon effective mass, unless the negative energy states (Dirac sea) are taken into account and the corresponding renormalization counter terms are properly treated. It is also shown that static properties as well as low frequency dynamical properties are not too much affected by vacuum polarization effects. However, renormalization is crucial for a correct description of high energy processes associated with the creation of scalar mesons or of particle-antiparticle pairs, even if the momentum transfer is small. Polarization effects lead to a reduction of the effective mass of the scalar meson in the medium. (author)