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Ashtekar Variables and Matter Coupling

M. Tsuda·T. Shirafuji·H. -J. Xie
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Abstract

It has been shown for low-spin fields that the use of only the self-dual part of the connection as basic variable does not lead to spurious equations or inconsistencies. We slightly generalize the form of the chiral Lagrangian of half-integer spin fields and express its imaginary part in a simple form. If the imaginary part is non-vanishing, it will lead to spurious equations. As an example, for (Majorana) Rarita-Schwinger fields the equations of motion of the torsion is solved and it is shown that it vanishes owing to the Fierz identity.

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M. Tsuda, T. Shirafuji, H. -J. Xie. 1995-01-20. Ashtekar Variables and Matter Coupling. https://arxiv.org/abs/gr-qc/9501021

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