2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/177977We argue that the demand of background independence in a quantum theory of gravity calls for an extension of standard geometric quantum mechanics. We discuss a possible kinematical and dynamical generalization of the latter by way of a quantum covariance of the state space. Specifically, we apply our scheme to the problem of a background independent formulation of Matrix Theory.9 pages, LaTeXHigh Energy Physics - TheoryGeneral Relativity and Quantum CosmologyQuantum Physicstext