  In terms of two-spinors a chiral formulation of general relativity with the
Ashtekar Lagrangian and its Hamiltonian formalism in which the basic dynamic
variables are the dyad spinors are presented. The extended Witten identities
are derived. A new expression of the Hamiltonian boundary term is obtained.
Using this expression and the extended Witten identities the proof of the
positive energy theorem is extended to a case including momentum and angular
momentum.
