Insight on confinement using scalar field interactions

The scalar field plays an fundamental role in the investigation of confinement property characterising many particle physics models. This is achieved by coupling this particle directly with gauge fields at the lagrangian level. We have adopted the same approach {[}10{]} to determine a potential as a perturbative series in terms of interquark distance. In order to introduce the gravitational effects and inspired from bag models, we implement a scalar field which interacts both with the vacuum and the electron field. In this context and with presence of the vacuum condensates, it is possible to derive a more accurate expression of the electron energy.