Concise symplectic formulation for tetrad gravity

TL;DR

This paper presents a straightforward symplectic formulation of tetrad gravity that clarifies the derivation of real Ashtekar variables and elucidates the roles of the Immirzi parameter and time gauge.

Contribution

It introduces a simple symplectic approach to tetrad gravity, providing a clearer derivation of Ashtekar variables and insights into key parameters.

Findings

Derivation of real Ashtekar variables from a symplectic formulation

Clarification of the role of the Immirzi parameter

Insights into the time gauge in tetrad gravity

Abstract

We discuss a simple symplectic formulation for tetrad gravity that leads to the real Ashtekar variables in a direct and transparent way. It also sheds light on the role of the Immirzi parameter and the time gauge.