# Quantum Information Metric and Berry Curvature from a Lagrangian Approach

## TL;DR

This paper introduces a Lagrangian-based formalism to compute quantum geometric tensor and Berry curvature, offering a comprehensive and novel approach applicable to various quantum systems.

## Contribution

It generalizes existing formalisms to enable calculation of geometrical phases using a Lagrangian approach, providing a new perspective in quantum geometry.

## Key findings

- Formalism applied to well-known quantum systems
- Provides a complete conceptual framework
- Enables computation of geometrical phases

## Abstract

We take as a starting point an expression for the quantum geometric tensor recently 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 different point of view of earlier works. Using our formalism, we show how this expression can be applied to well-known quantum mechanical systems.