A Spin Gauge Formulation of Gravity and a New View of Gravity-Matter Interactions (1111.3267v3)

Abstract: A first-order formulation of gravity is developed in which the fundamental fields consist of an SL(2,C) connection and two spinor-valued 1-forms. It is shown that the first term of an expansion of the Einstein-Hilbert action leads to an action for these fields which consists of dynamic L2 inner products of their covariant derivatives, resembling reasonable generalisations of the terms found in the actions of typical gauge theories on Minkowski spacetime. If additional terms corresponding to other forces and matter, formulated in the same manner, are then included, this approach may shed new light on interactions of gravity with matter and other force carriers.