The Study on Generalized Toda Mechanics System with Loop Algebra L(Dr)

  • In this paper,we generalize the Toda mechanics system with long range interaction to the case of Loop algebra l(Dr).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.
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  • [1] . Toda M. J. Phys. Soc. Japan, 1967, 22: 431-436; J. Phys. Soc. Japan,1967, 23: 501-5062. Calogero F. J. Math. Phys. , 1971, 12: 419-436; Erratum, 1996, 37:3646; Lett .Nuovo Cimento, 1975, 13: 411-4163. Moser J.Adv.Math. , 1975, 16: 197-220; Prog. in Math. , 8, Birkhauser, Basel, 1980, 233-2894. Ruijsenaars S N M. Schneider.Ann. Phys. , 1986, 170: 370-4055. Donagi R, Witten E. Nucl. Phys. , 1996, B460: 299-334; hep-th/95101016. Dijkgraaf R, Vafa C. Nucl. Phys. , 2002, B664: 3-20; hep-th/02062557. Toda M. J.Phys. Soc. Japan, 1967, 23: 501-5068. Castro-Alvaredo O A, Fring A. Applications of Quantum Integrable Systems, arXiv: hep-th/ 0301102.9. JIANG Jin-Huan, LI Ai-Min, LI Zi-Ping. HEP NP, 2003, 27 ( 6 ) :489-492 10. YANG Zhan-Ying, ZHEN Yi .HEP NP, 2000, 24( 6) : 484-48911. YANG Zhan-Ying, ZHAO Liu,ZHEN Yi.HEP NP, 2000, 24( 4) : 1-7 12. CHAO L. Commun. Theore. Phys. , 1993, 15: 221; CHAO L. , YANG ZY. Commun. Theore. Phys. , 2001, 35: 435; Hollowood T. Nucl. Phys. ,1992, B384: 52313. LIU Wang-Yun, YANG Zhan-Ying, ZHAO Liu. HEP NP, 2004, 28(4) : 359-36414. ZHAO Liu, LIU Wang-Yun. Commun.Theore. Phys. , 2004, 42: 9-1815. YANG Zhan-Ying, ZHAO Liu, LIU Wang-Yun et al. Generalized Toda Mechanics Associated with Loop Algebras L( Cr) and L( Dr ) and Their Reduct ions. Commun.Theore. Phys. , 2004, ( in press)
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ZHU Qiao, YANG Zhan-Ying and SHI Kang-Ji. The Study on Generalized Toda Mechanics System with Loop Algebra L(Dr)[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(Dr)[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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The Study on Generalized Toda Mechanics System with Loop Algebra L(Dr)

    Corresponding author: ZHU Qiao,
  • Institute of Modern Physics,Northwest University,Xi'an 710069,China

Abstract: In this paper,we generalize the Toda mechanics system with long range interaction to the case of Loop algebra l(Dr).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.

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