Covariant Hamiltonian dynamics

Holten, J.W. van

doi:10.1103/physrevd.75.025027

Cited by 54 publications

(95 citation statements)

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“…[23] based on Killing tensors. Our conserved quantity (3.29) is indeed associated to a fourth-rank Killing tensor -the only previously known examples being those discussed in…”

Section: Resultsmentioning

confidence: 99%

Separability and dynamical symmetry of Quantum Dots

et al. 2014

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The separability and Runge-Lenz-type dynamical symmetry of the internal dynamics of certain two-electron Quantum Dots, found by Simonović et al. [1], is traced back to that of the perturbed Kepler problem. A large class of axially symmetric perturbing potentials which allow for separation in parabolic coordinates can easily be found. Apart of the 2:1 anisotropic harmonic trapping potential considered in [1], they include a constant electric field parallel to the magnetic field (Stark effect), the ring-shaped Hartmann potential, etc. The harmonic case is studied in detail.

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“…[23] based on Killing tensors. Our conserved quantity (3.29) is indeed associated to a fourth-rank Killing tensor -the only previously known examples being those discussed in…”

Section: Resultsmentioning

confidence: 99%

Separability and dynamical symmetry of Quantum Dots

et al. 2014

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“…These equations were obtained by Sommers [10] and van Holten [11]. Several applications are found in [13].…”

Section: Formulation Of Generalized Killing Equationsmentioning

confidence: 98%

“…The explicit form of the Hamiltonian is given by (10), and the constraint equation is given by (11). Then the Killing hierarchy (20) reads…”

Section: Appendix A: Killing Hierarchy For a Free Particlementioning

confidence: 99%

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Constants of motion for constrained Hamiltonian systems: A particle around a charged rotating black hole

2011

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We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint, which arises from the reparametrization invariance of the particle orbit. As the necessary and sufficient condition for the existence of a constant of motion, we obtain a set of equations with a hierarchical structure, which is understood as a generalization of the Killing tensor equation. It is also a generalization of the conventional argument in that it includes the case when the conservation condition holds only on the constraint surface in the phase space. In that case, it is shown that the constant of motion is associated with a conformal Killing tensor. We apply the hierarchical equations and find constants of motion in the case of a charged particle in an electromagnetic field in black hole spacetimes. We also demonstrate that gravitational and electromagnetic fields exist in which a charged particle has a constant of motion associated with a conformal Killing tensor.

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“…In particular the canonical brackets (40) do not have a direct geometric representation. Manifestly covariant formulations of the dynamics do however exist [15]. In this section we develop actually two such formulations.…”

Section: Covariant Hamiltonian Formalismmentioning

confidence: 99%