Note on the phase space of asymptotically flat gravity in Ashtekar-Barbero variables

TL;DR

This paper characterizes the phase space of asymptotically flat gravity using Ashtekar-Barbero variables, deriving the Poincaré generators and introducing a polynomial rotation generator suitable for quantum theory.

Contribution

It demonstrates that the Gauss constraint multiplier must decay more slowly to recover ADM phase space and derives Poincaré generators without referencing ADM, including a polynomial rotation generator.

Findings

Gauss constraint multiplier decay rate adjusted for ADM recovery

Derived Poincaré generators within Ashtekar-Barbero phase space

Introduced a polynomial generator of asymptotic rotations

Abstract

We describe the canonical phase space of asymptotically flat gravity in Ashtekar-Barbero variables. We show that the Gauss constraint multiplier must fall off slower than previously considered in order to recover ADM phase space. The generators of the asymptotic Poincare group are derived within the Ashtekar-Barbero phase space without reference to the ADM generators. The resulting expressions are shown to agree, modulo Gauss constraint terms, with those obtained from the ADM generators. A payoff of this procedure is a new expression for the generator of asymptotic rotations which is polynomial in the triad and hence better suited for quantum theory. Our treatment complements earlier description by Thiemann in the context of self-dual variables.