Einstein-Cartan-Heisenberg Theory of Gravity with Dynamical Torsion

TL;DR

This paper proposes a new interpretation of Einstein-Cartan gravity where torsion is dynamical and related to a classical spinor field, leading to a model describing particles as geometric entities without charge or mass.

Contribution

It introduces a novel approach linking torsion and spinor fields, with a dynamical equation for torsion, and explores a spherically symmetric solution representing a massless, uncharged particle with spin.

Findings

Derived a spherically symmetric solution in the theory

Interpreted the solution as a geometric model of a particle

Connected torsion dynamics with classical spinor fields

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'').