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

Mück, Wolfgang

doi:10.1103/physrevd.97.025011

Cited by 6 publications

(7 citation statements)

References 5 publications

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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%

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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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Section: Higgsmentioning

confidence: 99%

“…where E d are eigenvalues of H The recursive solution of (35) proceeds as follows. First, the solution at d = 1 is given by (31) as…”

Section: The Superintegrable Rosochatius Systemmentioning

confidence: 99%

Mapping superintegrable quantum mechanics to resonant spacetimes

2018

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“…As we can see, the eigenvalues in Eq. (21) are given in terms of all the physical parameters of the problem, that is, all the physical quantities present in Klein-Gordon equation (4). However, these eigenvalues do not constitute the spectrum of the system.…”

Section: The Klein-gordon Equationmentioning

confidence: 99%

“…A procedure to construct generalized ladder operators for the Klein-Gordon equation with a scalar curvature term was obtained in Ref. [4]. Another interesting work addresses the study of nonlinear quantum electrostatic waves in a pseudorelativistic quantum semiconductor plasm [5].…”

Section: Introductionmentioning

confidence: 99%

Ground state of a bosonic massive charged particle in the presence of external fields in a Gödel-type spacetime

Silva

2018

Eur. Phys. J. Plus

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The relativistic quantum dynamics of a spinless charged particle interacting with both Aharonov-Bohm and Coulomb-type potentials in the Gödel-type spacetime is considered. The dynamics of the system is governed by the Klein-Gordon equation with interactions. We verify that it is possible to establish a quantum condition between the energy of the particle and the parameter that characterizes the vorticist of the spacetime. We rigorously analyze the ground state of the system and determine the corresponding wavefunctions to it.

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“…Many relevant systems described in terms of ladder operators have been discussed in the literature during many years. We refer here to the monograph [2], and to the papers [3]- [7], which are just few of those written in the past three years. This very partial list of references is sufficient to give an idea of the vitality of the topic, also in contexts which might appear quite non standard, see for instance [8] and [9].…”

Section: Introductionmentioning

confidence: 99%

Coupled Susy, pseudo-bosons and a deformed $\mathfrak{su}(1,1)$ Lie algebra

Bagarello

2021

Preprint

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In a recent paper a pair of operators a and b satisfying the equations a † a = bb † + γ1 1 and aa † = b † b + δ1 1, has been considered, and their nature of ladder operators has been deduced and analysed. Here, motivated by the spreading interest in non self-adjoint operators in Quantum Mechanics, we extend this situation to a set of four operators, c, d, r and s, satisfying dc = rs + γ1 1 and cd = sr + δ1 1, and we show that they are also ladder operators. We show their connection with biorthogonal families of vectors and with the so-called D-pseudo bosons. Some examples are discussed.

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

Cited by 6 publications

References 5 publications

Mapping superintegrable quantum mechanics to resonant spacetimes

Mapping superintegrable quantum mechanics to resonant spacetimes

Ground state of a bosonic massive charged particle in the presence of external fields in a Gödel-type spacetime

Coupled Susy, pseudo-bosons and a deformed $\mathfrak{su}(1,1)$ Lie algebra

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