General first-order mass ladder operators for Klein–Gordon fields

Cardoso, Vítor; Houri, Tsuyoshi; Kimura, Masashi

doi:10.1088/1361-6382/aa9a04

Cited by 10 publications

(7 citation statements)

References 23 publications

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“…It is known that the ladder operators in quantum mechanics are related to the underlying symmetry of a given system. As shown in [1,2], a similar discussion based on ladder operators from symmetry of spacetimes is possible for a Klein-Gordon field. Ladder operators of the massive Klein-Gordon field can be defined in spacetimes with a particular conformal symmetry, e.g., (anti-)de Sitter spacetimes, and these operators change the mass squared of the Klein-Gordon field [1,2].…”

Section: Introductionmentioning

confidence: 87%

“…As shown in [1,2], a similar discussion based on ladder operators from symmetry of spacetimes is possible for a Klein-Gordon field. Ladder operators of the massive Klein-Gordon field can be defined in spacetimes with a particular conformal symmetry, e.g., (anti-)de Sitter spacetimes, and these operators change the mass squared of the Klein-Gordon field [1,2]. The operator is named the mass ladder operator and allows to analyze the deeper structure of test fields in curved spacetimes [3,4] as ladder operators in quantum mechanics.…”

Section: Introductionmentioning

confidence: 87%

“…For example, for a test field in black hole spacetimes, appropriate boundary conditions at the horizon and infinity define its characteristic oscillation, namely, quasinormal ringing, which plays an important role in various contexts [12][13][14][15][16][17][18][19][20][21][22]. Naturally, the following question arises: Does a solution generated from a physically meaningful solution by the mass ladder operator [1,2] satisfy the appropriate boundary conditions that are the same as the original solution?…”

Section: Introductionmentioning

confidence: 99%

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Ladder operators and quasinormal modes in Bañados-Teitelboim-Zanelli black holes

Katagiri¹,

Kimura²

2022

Preprint

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We study quasinormal modes (QNMs) of massive Klein-Gordon fields in static Bañados-Teitelboim-Zanelli (BTZ) black holes in terms of ladder operators constructed from spacetime conformal symmetries. Because the BTZ spacetime is locally isometric to the three-dimensional anti-de Sitter spacetime, ladder operators, which map a solution of the massive Klein-Gordon equation into that with different mass squared, can be constructed from spacetime conformal symmetries. In this paper, we apply the ladder operators to the QNMs of the Klein-Gordon equations in the BTZ spacetime. We demonstrate that the ladder operators can change indices of QNM overtones, and all overtone modes can be generated from a fundamental mode when we impose the Dirichlet or Neumann boundary condition at infinity. We also discuss the case with the Robin boundary condition.

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

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Ladder operators and quasinormal modes in Bañados-Teitelboim-Zanelli black holes

Katagiri¹,

Kimura²

2022

Preprint

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“…It is tempting to conjecture that AdS (being a maximally symmetric spacetime) is the only spacetime with this property, though we do not know a proof. Relations between Klein-Gordon equations of different masses have recently surfaced in the literature on "mass ladder operators" [28][29][30][31].…”

Section: Higgsmentioning

confidence: 99%

Mapping superintegrable quantum mechanics to resonant spacetimes

2018

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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 differential geometry. As an illustration, we explicitly demonstrate how to apply this procedure to superintegrable Rosochatius systems, resulting in a large family of spacetimes with resonant spectra for massless wave equations.

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“…In two recent papers [1,2], Cardoso, Houri and Kimura constructed ladder operators for the Klein-Gordan equation in manifolds possessing closed conformal Killing vectors, which are, in addition, eigenvectors of the Ricci tensor. More precisely, they constructed a first order operator D such that, if Φ is a solution of…”

Section: Introductionmentioning

confidence: 99%

Ladder operators for the Klein-Gordon equation with a scalar curvature term

Mück¹

2018

Phys. Rev. D

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

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General first-order mass ladder operators for Klein–Gordon fields

Cited by 10 publications

References 23 publications

Ladder operators and quasinormal modes in Bañados-Teitelboim-Zanelli black holes

Ladder operators and quasinormal modes in Bañados-Teitelboim-Zanelli black holes

Mapping superintegrable quantum mechanics to resonant spacetimes

Ladder operators for the Klein-Gordon equation with a scalar curvature term

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