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

TL;DR

This paper derives Barbero's Hamiltonian formulation of general relativity from a generalized Hilbert-Palatini action, highlighting its real variables and connection to modified canonical variables.

Contribution

It provides a derivation of Barbero's Hamiltonian from a generalized action, clarifying its theoretical foundation and relation to earlier formulations.

Findings

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

The formulation uses real connection variables.

The approach clarifies the theoretical basis of Barbero's variables.

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.