Quantum information metric and Berry curvature from a Lagrangian approach

We take as a starting point an expression for the quantum geometric tensor re- cently derived in the context of the gauge/gravity duality. We proceed to generalize this formalism in such way it is possible to compute the geometrical phases of quantum systems. Our scheme provides a conceptually complete description and introduce a dif- ferent point of view of earlier works. Using our formalism, we show how this expression can be applied to well-known quantum mechanical systems.