Time reparametrization group and the long time behaviour in quantum glassy systems

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations, and within this language the long time behaviour of this model is controlled by a reparametrization group (R${}_p$G) fixed point of the classical dynamics. The irrelevance of the quantum terms in the dynamical equations in the aging regime explains the classical nature of the violation of the fluctuation-dissipation theorem.