Self-dual teleparallel formulation of general relativity and the positive energy theorem

A self-dual and anti-self-dual decomposition of the teleparallel formulation of Einstein’s general relativity is carried out and the self-dual Lagrangian of the teleparallel formulation of Einstein’s general relativity, 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 the gauge condition of Nester and co-workers 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 and co-workers is extended to a case including momentum.