Self-Dual Action for Fermionic Fields and Gravitation

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

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13 pages, plain-tex, recently appearing in Nuovo Cimento B, volume 109, pages 973-982, September 1994

Scientific paper

10.1007/BF02726144

This paper studies the self-dual Einstein-Dirac theory. A generalization is obtained of the Jacobson-Smolin proof of the equivalence between the self-dual and Palatini purely gravitational actions. Hence one proves equivalence of self-dual Einstein-Dirac theory to the Einstein-Cartan-Sciama-Kibble-Dirac theory. The Bianchi symmetry of the curvature, core of the proof, now contains a non-vanishing torsion. Thus, in the self-dual framework, the extra terms entering the equations of motion with respect to the standard Einstein-Dirac field equations, are neatly associated with torsion.

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