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

Abstract

The hierarchy of conformally coupled scalars with the increasing scaling dimensions ${\Delta }_k=k-d/2$, $k=1,2,3,...$ connected with the $k$-th Euler density in the corresponding space-time dimensions $d\ge 2k$ 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.

Latex, 11 pages, v.2, two misprints corrected

References in corpus (1)

• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)

Cited by in corpus (3)

• Conformal invariant powers of the Laplacian, Fefferman-Graham ambient metric and Ricci gauging
• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians
• Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants