Hamiltonian form of Carroll gravity

Abstract

We develop a Hamiltonian description of the ``Carroll'' (Levy Leblond-Sen Gupta) limit of gravity theory in the first-order formalism. Through a constraint analysis, the number of local degrees of freedom are shown to be two in this singular limit. The Hamiltonian constraint in this (``magnetic'') limit depends only on the densitized triad fields and their space derivatives. We also provide a scaling prescription within the Hilbert-Palatini theory to obtain the first-order analogue of the ``electric'' limit of canonical metric gravity. The simplicity of both these limiting Hamiltonian forms in these variables make them interesting candidates for quantization.