  By making use of the Langevin dynamics and its generating functional (GF)
formulation the influence of the long-range nature of the interaction on the
tendency of the glass formation is systematically investigated. In doing so two
types of models is considered: (i) the non-disordered model with a pure
repulsive type of interaction and (ii) the model with a randomly distributed
strength of interaction (a quenched disordered model). The long-ranged
potential of interaction is scaled with a number of particles $N$ in such a way
as to enable for GF the saddle-point treatment as well as the systematic 1/N -
expansion around it. We show that the non-disordered model has no glass
transition which is in line with the mean-field limit of the mode - coupling
theory (MCT) predictions. On the other hand the model with a long-range
interaction which above that has a quenched disorder leads to MC - equations
which are generic for the $p$ - spin glass model and polymeric manifold in a
random media.
