Spontaneous generation of eigenvalues

Details Spontaneous generation of eigenvalues Spontaneous generation of eigenvalues

2005-06-02

arxiv.org/abs/math/0506047v1

Mathematics

Differential Geometry

19 pages, LaTeX

Scientific paper

10.1016/j.geomphys.2005.12.001

We show that the action of conformal vector fields on functions on the sphere determines the spectrum of the Laplacian (or the conformal Laplacian), without further input of information. The spectra of intertwining operators (both differential and non-local) with principal part a power of the Laplacian follows as a corollary. An application of the method is the sharp form of Gross' entropy inequality on the sphere. The same method gives the spectrum of the Dirac operator on the sphere, as well as of a continuous family of nonlocal intertwinors, and an infinite family of odd-order differential intertwinors.

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