Invariants and nonlinear fields in Spinor Gravity

TL;DR

This paper explores spinor gravity, a formulation where gravity emerges from fundamental spinor fields, leading to modified Einstein equations due to new invariants and emphasizing nonlinear geometric aspects.

Contribution

It introduces a novel approach to gravity based solely on spinor fields, highlighting the role of invariants and nonlinear fields in the effective gravitational equations.

Findings

Effective gravitational equations are derived from the lowest order Schwinger-Dyson equation.

New invariants modify Einstein's equations in spinor gravity.

Different geometric viewpoints elucidate the role of nonlinear fields.

Abstract

Spinor gravity is a functional integral formulation of gravity based only on fundamental spinor fields. The vielbein and metric arise as composite objects. Due to the lack of local Lorentz-symmetry new invariants in the effective gravitational action lead to a modification of Einstein's equations. We discuss different geometrical viewpoints of spinor gravity with particular emphasis on nonlinear fields. The effective gravitational field equations arise as solutions to the lowest order Schwinger-Dyson equation for spinor gravity.