Darboux coordinates for (first order) tetrad gravity

TL;DR

This paper explores the Hamiltonian formulation of first order tetrad gravity, introducing a non-linear transformation of variables to clarify the geometric and constraint structure of the theory.

Contribution

It presents a novel non-linear field redefinition that isolates conjugate variables in the Hamiltonian form of tetrad gravity, enhancing understanding of its geometric constraints.

Findings

Identifies a specific non-linear transformation of variables.

Clarifies the geometric interpretation of constraints.

Provides insights into the canonical structure of tetrad gravity.

Abstract

The Hamiltonian form of the Hilbert action in the first order tetrad formalism is examined. We perform a non-linear field redefinition of the canonical variables isolating the part of the spin connection which is canonically conjugate to the tetrad. The geometrical meaning of the constraints written in these new variables is examined.