Einstein-Cartan-Heisenberg Theory of Gravity with Dynamical Torsion

Abstract

On the basis of an algebraic relation between torsion and a classical spinor field a new interpretation of Einstein-Cartan gravity interacting with classical spinor field is proposed. In this approach the spinor field becomes an auxiliary field and the dynamical equation for this field (the Heisenberg equation) is a dynamical, gravitational equation for torsion. The simplest version of this theory is examined where the metric degrees of freedom are frozen and only torsion plays a role. A spherically symmetric solution of this theory is examined. This solution can be interpreted, in the spirit of Wheeler's ideas of ``charge without charge'' and ``mass without mass'', as a geometrical model for an uncharged and massless particle with spin (``spin without spin'').