Boundary term, extended Witten identities and positivity of energy

TL;DR

This paper presents a spinor-based formulation of general relativity, derives extended Witten identities, and proves the positive energy theorem including momentum and angular momentum.

Contribution

It introduces a new boundary term expression and extends the positive energy proof using extended Witten identities in a spinor framework.

Findings

Derived extended Witten identities.

Obtained a new expression for the Hamiltonian boundary term.

Extended positive energy theorem to include momentum and angular momentum.

Abstract

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.