Canonical Vielbeins for General Relativity: D + 1 Decomposition and Constraint Analysis
arXiv:2602.18491
Abstract
We provide a self-contained derivation of the Hamiltonian formulation of General Relativity in vielbein variables in dimensions. Starting from the Einstein--Hilbert action in a standard metric decomposition, we derive Lorentz- and -covariant phase-space actions, identify the primary Lorentz constraints, and obtain the Hamiltonian and momentum constraints. We compute the resulting first-class constraint algebra, relate the vielbein and metric phase-space formulations, and discuss the rotation/boost decomposition. In particular, we construct the boost generator in the -covariant formulation, thereby recovering full local Lorentz symmetry.
33 pages, subsection added "Castellani Generators", minor corrections, Submission to SciPost