2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35017A self-dual and anti-self-dual decomposition of the teleparallel gravity is carried out and the self-dual Lagrangian of the teleparallel gravity which is equivalent to the Ashtekar Lagrangian in vacuum is obtained. Its Hamiltonian formulation and the constraint analysis are developed. Starting from Witten's equation Nester's gauge condition is derived directly and a new expression of the boundary term is obtained. Using this expression and Witten's identity the proof of the positive energy theorem by Nester et al is extended to a case including momentum.11 pages, no figureGeneral Relativity and Quantum Cosmologytext