Comment on Holst’s Lagrangian formulation

Abstract

We make two observations about Holst’s derivation of Barbero’s Hamiltonian formulation from a covariant Lagrangian. While Holst’s derivation does appear to be correct, there are two points in the derivation which may be worth clarifying. These concern the choice of time gauge and the manner in which the Hamiltonian variables are defined in terms of the covariant ones. We emphasize that our observations in no way affect the validity of Holst’s result.