Time-dependent realization of the infinite-dimensional hydrogen algebra

Jamil Daboul; Pavel Winternitz

doi:10.1016/S0375-9601(01)00166-9

Time-dependent realization of the infinite-dimensional hydrogen algebra

Jamil Daboul, Pavel Winternitz

Department of Physics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We use the Hamiltonian formalism to investigate the Katzin-Levine model of a time-dependent Kepler problem. This formalism enables us to define Lie products in terms of Poisson brackets and obtain a time-dependent realization of centerless twisted (or standard) Kac-Moody algebras of so(N + 1). We also show that the classical solutions of the model are modulated conic sections and derive a generalized Kepler equation for the time dependence.

Original language	English
Pages (from-to)	163-168
Number of pages	6
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	282
Issue number	3
DOIs	https://doi.org/10.1016/S0375-9601(01)00166-9
State	Published - 16 Apr 2001

Keywords

Kac-Moody algebras
Kepler equation
Runge-Lenz vector
Super-integrable Hamiltonians
Time-dependent Hamiltonians

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/S0375-9601(01)00166-9

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title = "Time-dependent realization of the infinite-dimensional hydrogen algebra",

abstract = "We use the Hamiltonian formalism to investigate the Katzin-Levine model of a time-dependent Kepler problem. This formalism enables us to define Lie products in terms of Poisson brackets and obtain a time-dependent realization of centerless twisted (or standard) Kac-Moody algebras of so(N + 1). We also show that the classical solutions of the model are modulated conic sections and derive a generalized Kepler equation for the time dependence.",

keywords = "Kac-Moody algebras, Kepler equation, Runge-Lenz vector, Super-integrable Hamiltonians, Time-dependent Hamiltonians",

author = "Jamil Daboul and Pavel Winternitz",

note = "Funding Information: We are grateful to Dr. Faruk G{\"u}ngor for drawing our attention to the paper of Katzin and Levine. The research of P.W. is partially supported by a research grant from NSERC of Canada. ",

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AU - Daboul, Jamil

AU - Winternitz, Pavel

N1 - Funding Information: We are grateful to Dr. Faruk Güngor for drawing our attention to the paper of Katzin and Levine. The research of P.W. is partially supported by a research grant from NSERC of Canada.

PY - 2001/4/16

Y1 - 2001/4/16

N2 - We use the Hamiltonian formalism to investigate the Katzin-Levine model of a time-dependent Kepler problem. This formalism enables us to define Lie products in terms of Poisson brackets and obtain a time-dependent realization of centerless twisted (or standard) Kac-Moody algebras of so(N + 1). We also show that the classical solutions of the model are modulated conic sections and derive a generalized Kepler equation for the time dependence.

AB - We use the Hamiltonian formalism to investigate the Katzin-Levine model of a time-dependent Kepler problem. This formalism enables us to define Lie products in terms of Poisson brackets and obtain a time-dependent realization of centerless twisted (or standard) Kac-Moody algebras of so(N + 1). We also show that the classical solutions of the model are modulated conic sections and derive a generalized Kepler equation for the time dependence.

KW - Kac-Moody algebras

KW - Kepler equation

KW - Runge-Lenz vector

KW - Super-integrable Hamiltonians

KW - Time-dependent Hamiltonians

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U2 - 10.1016/S0375-9601(01)00166-9

DO - 10.1016/S0375-9601(01)00166-9

M3 - Article

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SN - 0375-9601

VL - 282

SP - 163

EP - 168

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 3

ER -

Time-dependent realization of the infinite-dimensional hydrogen algebra

Abstract

Keywords

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