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arXiv · 1710.01283

Ladder operators for Klein-Gordon equation with scalar curvature term

Wolfgang Mück
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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.

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Wolfgang Mück. 2017-10-03. Ladder operators for Klein-Gordon equation with scalar curvature term. https://doi.org/10.1103/physrevd.97.025011

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