Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action

TL;DR

Barbero’s Hamiltonian formulation is derived from an action, which can be considered as a generalization of the ordinary Hilbert-Palatini action, and provides a real theory of gravity with a connection as configuration variable, and with the usual Gauss and vector constraint.

Abstract

Barbero recently suggested a modification of Ashtekar's choice of canonical variables for general relativity. Although leading to a more complicated Hamiltonian constraint this modified version, in which the configuration variable still is a connection, has the advantage of being real. In this article we derive Barbero's Hamiltonian formulation from an action, which can be considered as a generalization of the ordinary Hilbert-Palatini action.