A Quadratic Spinor Lagrangian for General Relativity

TL;DR

This paper introduces a novel quadratic spinor Lagrangian for Einstein gravity, establishing a covariant Hamiltonian formulation that relates to the Einstein-Hilbert action and supports quasi-local energy-momentum definitions.

Contribution

It presents a new finite, quadratic spinor Lagrangian for General Relativity with a covariant Hamiltonian, connecting to the Einstein-Hilbert action via a total differential.

Findings

Lagrangian is quadratic in the covariant derivative of a spinor field.

Establishes a spinor-curvature identity relating to Einstein-Hilbert Lagrangian.

Defines a covariant Hamiltonian for quasi-local energy-momentum.

Abstract

We present a new finite action for Einstein gravity in which the Lagrangian is quadratic in the covariant derivative of a spinor field. Via a new spinor-curvature identity, it is related to the standard Einstein-Hilbert Lagrangian by a total differential term. The corresponding Hamiltonian, like the one associated with the Witten positive energy proof is fully four-covariant. It defines quasi-local energy-momentum and can be reduced to the one in our recent positive energy proof. (Fourth Prize, 1994 Gravity Research Foundation Essay.)