From Holst to Carroll gravity: A Hamiltonian point of view
Phys. Rev. D 114, 065024 – Published 23 September, 2026
DOI: https://doi.org/10.1103/cph1-yj1s
Abstract
In this paper, we present a comprehensive Hamiltonian analysis of a Carroll-invariant Lagrangian derived from the Holst action. To guide the analysis, Cartan geometry tools are used. We identify the full constraint structure of the theory, characterize its gauge symmetries, obtain the explicit form of the Hamiltonian vector fields, and introduce Ashtekar-like variables for the magnetic Carrollian regime. We also discuss in detail an analog of the time gauge employed in the Hamiltonian analysis of the Holst action for general relativity.
