  We provide a compact derivation of the static and dynamic equations for
infinite-dimensional particle systems in the liquid and glass phases. The
static derivation is based on the introduction of an "auxiliary" disorder and
the use of the replica method. The dynamic derivation is based on the general
analogy between replicas and the supersymmetric formulation of dynamics. We
show that static and dynamic results are consistent, and follow the Random
First Order Transition scenario of mean field disordered glassy systems.
