# Lagrangian and Hamiltonian formulations of the Palatini action

## TL;DR

This paper derives Ashtekar-Barbero variables in Loop Quantum Gravity from the Palatini action, highlighting the necessity of torsion-free or compatibility conditions to accurately describe General Relativity.

## Contribution

It provides a derivation of key variables in LQG directly from the Palatini formulation, clarifying the conditions needed for a consistent description of gravity.

## Key findings

- Ashtekar-Barbero variables derived from Palatini action
- Torsion-free or compatibility condition required
- Clarifies foundational aspects of LQG

## Abstract

We derive the Ashtekar-Barbero variables in Loop Quantum Gravity(LQG) starting from the Palatini action. We find that we need either the torsion-free condition or the compatibility condition for the Palatini action to describe General Relativity.

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Source: https://tomesphere.com/paper/1706.07301