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arXiv · 2210.04837

Second-Order, Biconformally Invariant Scalar-Tensor Field Theories in a Four-Dimensional Space

Gregory W. Horndeski
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Abstract

In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be derivable from a variational principle using a Lagrange scalar density which is a concomitant of the field variables and their derivatives of arbitrary, but finite, order. I shall consider biconformal transformations of the field variables, which are conformal transformations which affect both the metric tensor and scalar field. A necessary and sufficient condition will be developed to determine when the Euler-Lagrange tensor densities are biconformally invariant. This condition will be employed to construct all of the second-order biconformally invariant scalar-tensor field theories in a space of four-dimensions. It turns out that the field equations of these theories can be derived from a linear combination of (at most) two second-order Lagrangians, with the coefficients in that linear combination being real constants.

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Gregory W. Horndeski. 2022-10-10. Second-Order, Biconformally Invariant Scalar-Tensor Field Theories in a Four-Dimensional Space. https://arxiv.org/abs/2210.04837

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