  Diakonov formulated a model of a primordial Dirac spinor field interacting
gravitationally within the geometric framework of the Poincar\'e gauge theory
(PGT). Thus, the gravitational field variables are the orthonormal coframe
(tetrad) and the Lorentz connection. A simple gravitational gauge Lagrangian is
the Einstein-Cartan choice proportional to the curvature scalar plus a
cosmological term. In Diakonov's model the coframe is eliminated by expressing
it in terms of the primordial spinor. We derive the corresponding field
equations for the first time. We extend the Diakonov model by additionally
eliminating the Lorentz connection, but keeping local Lorentz covariance
intact. Then, if we drop the Einstein-Cartan term in the Lagrangian, a
nonlinear Heisenberg type spinor equation is recovered in the lowest
approximation.
