## Klein-Gordonization. (arXiv:1711.03297v1 [hep-th])

We describe a procedure naturally associating relativistic Klein-Gordon
equations in static curved spacetimes to non-relativistic quantum motion on
curved spaces in the presence of a potential. Our procedure is particularly
attractive in application to (typically, superintegrable) problems whose energy
spectrum is given by a quadratic function of the energy level number, since for
such systems the spacetimes one obtains possess evenly spaced, resonant spectra
of frequencies for scalar fields of a certain mass. This construction emerges
as a generalization of the previously studied correspondence between the Higgs
oscillator and Anti-de Sitter spacetime, which has been useful for both
understanding weakly nonlinear dynamics in Anti-de Sitter spacetime and
algebras of conserved quantities of the Higgs oscillator. Our conversion
procedure ("Klein-Gordonization") reduces to a nonlinear elliptic equation
closely reminiscent of the one emerging in relation to the celebrated Yamabe
problem of查看全文