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doi:10.1016/S0375-9601(99)00282-0 
Einstein–Cartan–Heisenberg theory of gravity with dynamical torsion
Received 22 October 1998;
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Abstract
On the basis of an algebraic relation between torsion and a classical spinor field a new interpretation of Einstein–Cartan gravity interacting with a 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 particle with spin (“spin without spin”).
