Ladder operators for Klein-Gordon equation with scalar curvature term

Abstract

Recently, Cardoso, Houri and Kimura constructed generalized ladder operators for massive Klein-Gordon scalar fields in space-times with conformal symmetry. Their construction requires a closed conformal Killing vector, which is also an eigenvector of the Ricci tensor. Here, a similar procedure is used to construct generalized ladder operators for the Klein-Gordon equation with a scalar curvature term. It is proven that a ladder operator requires the existence of a conformal Killing vector, which must satisfy an additional property. This property is necessary and sufficient for the construction of a ladder operator. For maximally symmetric space-times, the results are equivalent to those of Cardoso, Houri and Kimura.

8 pages, v2: version to appear in PRD

References in corpus (2)

• Mass Ladder Operators from Spacetime Conformal Symmetry
• General first-order mass ladder operators for Klein-Gordon fields

Cited by in corpus (2)

• Klein-Gordonization: mapping superintegrable quantum mechanics to resonant spacetimes
• Extended coupled SUSY, pseudo-bosons and weak squeezed states