Spinor One-forms as Gravitational Potentials

TL;DR

This paper presents a novel formulation of general relativity using spinor one-forms as gravitational potentials, deriving the metric and action from these spinor fields, and connecting to Hamiltonian and mass concepts.

Contribution

It introduces a new spinor-based action for general relativity using either 2-component or Dirac spinor one-forms, differing from traditional formulations.

Findings

The metric is quadratic in the spinor one-forms.

The action differs from the chiral action by a total differential.

The Hamiltonian relates to positive energy proofs and quasilocal mass.

Abstract

General relativity is derived from an action which is quadratic in the covariant derivative of certain spinor one-form gravitational potentials. Either a pair of 2-component spinor one-forms or a single Dirac spinor one-form can be employed. The metric is a quadratic function of these spinor one-forms. In the 2-component spinor formulation the action differs from the usual chiral action for general relativity by a total differential. In the Dirac spinor formulation the action is the real part of the former one. The Hamiltonian is related to the ones in positive energy proofs and spinorial quasilocal mass constructions.