### Abstract

It is well-known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This is achieved by constructing a Lagrangian with gauge symmetry in such a way that, by means of the Dirac algorithm, this Lagrangian reproduces the Adler-Kostant-Symes system whose Hamiltonian is the quadratic form associated with the scalar product on the Lie algebra.

Original language | English |
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Pages (from-to) | 58-64 |

Number of pages | 7 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 301 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Aug 19 2002 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Adler-Kostant-Symes systems as Lagrangian gauge theories.** / Fehér, L.; Gábor, A.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 301, no. 1-2, pp. 58-64. https://doi.org/10.1016/S0375-9601(02)00978-7

}

TY - JOUR

T1 - Adler-Kostant-Symes systems as Lagrangian gauge theories

AU - Fehér, L.

AU - Gábor, A.

PY - 2002/8/19

Y1 - 2002/8/19

N2 - It is well-known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This is achieved by constructing a Lagrangian with gauge symmetry in such a way that, by means of the Dirac algorithm, this Lagrangian reproduces the Adler-Kostant-Symes system whose Hamiltonian is the quadratic form associated with the scalar product on the Lie algebra.

AB - It is well-known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This is achieved by constructing a Lagrangian with gauge symmetry in such a way that, by means of the Dirac algorithm, this Lagrangian reproduces the Adler-Kostant-Symes system whose Hamiltonian is the quadratic form associated with the scalar product on the Lie algebra.

UR - http://www.scopus.com/inward/record.url?scp=0037136250&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037136250&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(02)00978-7

DO - 10.1016/S0375-9601(02)00978-7

M3 - Article

AN - SCOPUS:0037136250

VL - 301

SP - 58

EP - 64

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

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

SN - 0375-9601

IS - 1-2

ER -