The Study on Generalized Toda Mechanics System with Loop Algebra L(D<SUP>r</SUP>)

ZHU Qiao; YANG Zhan-Ying; SHI Kang-Ji

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2005, Vol. 29> Issue(1) : 19-22

The Study on Generalized Toda Mechanics System with Loop Algebra L(D^r)

Institute of Modern Physics,Northwest University,Xi'an 710069,China

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Abstract：
In this paper,we generalize the Toda mechanics system with long range interaction to the case of Loop algebra l(D^r).by using a pair of ordered positive integer (X,y) to describe Toda chains,we extract the equation of motion and the hamiltonian structure of this system for (3,2) Toda chain.it turns out that both extra coordinates and standard Toda variables are Poisson non–commutative in the case of nontrivial generalization,and for some case,extra variables appear linearly on the right hand side of the Poisson bracket.

References

[1]

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ZHU Qiao, YANG Zhan-Ying and SHI Kang-Ji. The Study on Generalized Toda Mechanics System with Loop Algebra L(D^r)[J]. Chinese Physics C, 2005, 29(1): 19-22.

ZHU Qiao, YANG Zhan-Ying and SHI Kang-Ji. The Study on Generalized Toda Mechanics System with Loop Algebra L(D^r)[J]. Chinese Physics C, 2005, 29(1): 19-22. shu

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Received: 2004-05-21
Revised: 2004-07-21

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沈阳化工大学材料科学与工程学院沈阳 110142

The Study on Generalized Toda Mechanics System with Loop Algebra L(D^r)

Corresponding author: ZHU Qiao,

Institute of Modern Physics,Northwest University,Xi'an 710069,China

Received Date: 2004-05-21
Accepted Date: 2004-07-21
Available Online: 2005-01-05

Abstract: In this paper,we generalize the Toda mechanics system with long range interaction to the case of Loop algebra l(D^r).by using a pair of ordered positive integer (X,y) to describe Toda chains,we extract the equation of motion and the hamiltonian structure of this system for (3,2) Toda chain.it turns out that both extra coordinates and standard Toda variables are Poisson non–commutative in the case of nontrivial generalization,and for some case,extra variables appear linearly on the right hand side of the Poisson bracket.