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.
Ladder operators for the Klein-Gordon equation with a scalar curvature term / Mück, Wolfgang. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - 97:2(2018), p. 025011. [10.1103/PhysRevD.97.025011]
Ladder operators for the Klein-Gordon equation with a scalar curvature term
Mück, Wolfgang
2018
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.File | Dimensione | Formato | |
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