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We will consider the most general least-order derivative action for thetorsional completion of gravitational backgrounds filled with left-handed andright-handed semi-spinorial fields, accounting for all parity-even as well asparity-odd contributions; we will proceed by performing the customary analysis,decomposing torsion and substituting it in terms of the semi-spinorial densitycurrents, in order to obtain the effective action with the torsionally-inducedself-interacting potentials among the chiral fermionic fields: we shall seethat the resulting effective non-linear potentials will turn eventually out tobe parity conserving after all.

Least-Order Torsion-Gravity for Chiral-Spinor Fields, induced Self-Interacting Potentials and Parity Conservation