Invariants and nonlinear fields in Spinor Gravity

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.