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Conformal coupling of the scalar field with gravity in higher dimensions and invariant powers of the Laplacian

Ruben Manvelyan·D. H. Tchrakian
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Abstract

The hierarchy of conformally coupled scalars with the increasing scaling dimensions $Δ_{k}=k-d/2$, $k=1,2,3,... $ connected with the $k$-th Euler density in the corresponding space-time dimensions $d\geq 2k$ is proposed. The corresponding conformal invariant Lagrangian with the $k$-th power of Laplacian for the already known cases $k=1,2$ is reviewed, and the subsequent case of $k=3$ is completely constructed and analyzed.

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Ruben Manvelyan, D. H. Tchrakian. 2007-07-12. Conformal coupling of the scalar field with gravity in higher dimensions and invariant powers of the Laplacian. https://doi.org/10.1016/j.physletb.2006.12.027

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