Canonical and symplectic analysis of the Holst action in the $G\rightarrow 0$ limit

Abstract

By using the Dirac and symplectic formalisms, the analysis of the Holst action in the $G \rightarrow 0$ limit is performed. We study the theory's full canonical structure and symmetries. In particular, we focus on the cases $γ= i$ and $γ\neq i$, aiming to obtain Smolin's auto-self-dual model in terms of the Ashtekar variables and a Barbero-type formulation. We then perform the symplectic analysis and discuss the principal insight of these formalisms.