The Walecka many-body field theory is investigated in the context of quantum nonextensive statistical mechanics, characterized by a dimensionless parameter q. In this paper, we consider nuclear matter described statistically by a power-law distribution which generalizes the standard Fermi-Dirac distribution (q = 1). We show that the scalar and vector meson fields become more intense due to the nonextensive effects (q = 1). From a numerical treatment, we also show that as the nonextensive parameter q increases, the nucleon effective mass diminishes and the equation of state becomes stiffer. Finally, the usual Maxwell construction seems not to be necessary for isotherms with temperatures in the range 14Mev < kBT < 20MeV.

The eikonal profile function J(b) obtained from the Model of the Stochastic Vacuum is parametrized in a form suitable for comparison with experiment. The amplitude and the extended profile function (including imaginary and real parts) are determined directly from the complete pp andpp elastic scattering data at high energies. Full and accurate representation of the data is presented, with smooth energy dependence of all parameters. The changes needed in the original profile function required for description of scattering beyond the forward direction are described.

By using a q-calculus, the Walecka many-body field theory was studied in the context of the Tsallis framework. The most important aspect of the application of the q-calculus to the nonadditive formulation of QHD-I is that it naturally emerges as a thermodynamically consistent theory.