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Non-Minimally Coupled Scalar Field and Ashtekar Variables

Riccardo Capovilla
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Abstract

The non-minimal coupling of a scalar field is considered in the framework of Ashtekar's new variables formulation of gravity. A first order action functional for this system is derived in which the field variables are a tetrad field, and an SL(2,C) connection, together with the scalar field. The tetrad field and the SL(2,C) connection are related to the Ashtekar variables for the vacuum case by a conformal transformation. A canonical analysis shows that for this coupling the equations of Ashtekar's formulation of canonical gravity are non-polynomial in the scalar field. (to be published in Phys. Rev. D)

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Riccardo Capovilla. 1992-07-20. Non-Minimally Coupled Scalar Field and Ashtekar Variables. https://doi.org/10.1103/physrevd.46.1450

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