Self-consistent torsion potentials

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Abstract
The absence of an autonomous dynamics for the torsion field in the usual version of the Einstein-Cartan theory can be avoided through introduction of torsion potentials which yield the contortion tensor upon covariant differentiation. The ensuing self-consistency problem is solved in closed form for the special case of totally antisymmetric contortion tensor. The gauge-invariant feature of the torsion potentials, in the weak-field approximation, is the propagation of a longitudinal massless tordion mode whose parity is that of an axial vector.

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