Hamiltonian analysis of pregeometric gravity
Phys. Rev. D 112, 064058 – Published 19 September, 2025
DOI: https://doi.org/10.1103/v5wg-sy4w
Abstract
The Einstein-Cartan theory of gravity can arise from a mechanism of spontaneous symmetry breaking within the context of pregeometric gauge theories. In this work, we develop the Hamiltonian analysis of such theories. By making contact with the Arnowitt-Deser-Misner formalism, we show that all the results of canonical General Relativity are correctly recovered in the IR limit of the spontaneously broken phase. We then apply Dirac’s algorithm to study the algebra of constraints and determine the number of degrees of freedom in the UV limit of the unbroken phase. We also discuss possible pathways toward a UV completion of General Relativity, including a pregeometric generalization of the Wheeler-DeWitt equation and an extended BF formulation of the pregeometric theory.
