The conformally invariant Laplace–Beltrami operator and factor ordering

The conformally invariant Laplace-Beltrami operator and factor ordering

In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the Laplace-Beltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple factor orderings and show that the only other solution for a conformally flat metric is the conformally invariant Laplace-Beltrami operator. For non-conformal...

Conformally invariant powers of the ambient Dirac operator

Recent work in even-dimensional conformal geometry [1],[3], [4], [6] has revealed the importance of conformally invariant powers of the Laplacian on a conformal manifold; that is, of operators Pk whose principal part is the same as ∆ k with respect to a representative of the conformal structure. These invariant powers of the Laplacian were first defined in [5] in terms of the Fefferman-Graham [...

Is mass conformally invariant ?

By using the Garfinkle, Horowitz and Strominger black hole solutions as examples, we illustrate that, with respect to the reference action functional proposed by Hawking and Horowitz, the asymp-totic mass parameter is not invariant between two conformally related static spherically symmetric metrics.

Minimization of Conformally Invariant Energies

Conformally Invariant Non-local Operators

On a conformal manifold with boundary, we construct conformally invariant local boundary conditions B for the conformally invariant power of the Laplacian k , with the property that ( k , B) is formally self-adjoint. These boundary problems are used to construct conformally invariant nonlocal operators on the boundary Σ, generalizing the conformal Dirichlet-to-Robin operator, with principal par...