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Rarita-Schwinger Potentials in Quantum Cosmology

G. Esposito·G. Gionti·A. Yu. Kamenshchik·I. V. Mishakov·G. Pollifrone
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Abstract

This paper studies the two-spinor form of the Rarita-Schwinger potentials subject to local boundary conditions compatible with local supersymmetry. The massless Rarita-Schwinger field equations are studied in four-real-dimensional Riemannian backgrounds with boundary. Gauge transformations on the potentials are shown to be compatible with the field equations providing the background is Ricci-flat, in agreement with previous results in the literature. However, the preservation of boundary conditions under such gauge transformations leads to a restriction of the gauge freedom. The recent construction by Penrose of secondary potentials which supplement the Rarita-Schwinger potentials is then applied. The equations for the secondary potentials, jointly with the boundary conditions, imply that the background four-geometry is further restricted to be totally flat.

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G. Esposito, G. Gionti, A. Yu. Kamenshchik, I. V. Mishakov, G. Pollifrone. 1996-06-03. Rarita-Schwinger Potentials in Quantum Cosmology. https://arxiv.org/abs/gr-qc/9504013

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