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

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

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

Abstract
HTML
Reference
Related

PDF

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]

. 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)

[1]	SUN Yi , ZHANG Hao-Ran . One loop integrals reduction. Chinese Physics C, 2012, 36(11): 1055-1064. doi: 10.1088/1674-1137/36/11/004
[2]	CHEN Jia-Er , GUO Zhi-Yu , LU Yuan-Rong , GAO Shu-Li , ZHU Kun , WANG Zhi , YAN Xue-Qing , PENG Shi-Xiang , ZHAO Jie , GUO Ju-Fang , LI Wei-Guo , YU Mao-Lin , YUAN Zhong-Xi , FANG Jia-Xun . R&D Status of SFRFQ Accelerating System. Chinese Physics C, 2008, 32(S1): 231-233.
[3]	CHEN Li-Hua , CUI Bao-Qun , JIANG Wei-Sheng , LI Ai-Ling . Calculation of Extraction System of Ion Sources. Chinese Physics C, 2008, 32(S1): 304-306.
[4]	GENG Zhe-Qiao , Michizono Shinichiro , Matsumoto Toshihiro . Study of the Digital LLRF System for STF. Chinese Physics C, 2007, 31(8): 774-777.
[5]	FANG De-Qing , MA Yu-Gang , MA Chun-Wang , ZHONG Chen , CAI Xiang-Zhou , CHEN Jin-Gen , GUO Wei , SU Qian-Min , TIAN Wen-Dong , WANG Kun , YAN Ting-Zhi , SHEN Wen-Qing . Systematic Behavior of Isospin Effect in Fragmentation Reactions. Chinese Physics C, 2007, 31(1): 59-64.
[6]	YIN Zhong-Bao , ZHOU Dai-Cui . Performance of the ALICE PHOS Front-End Electronics. Chinese Physics C, 2006, 30(12): 1165-1170.
[7]	JIANG Yun-Guo , HUANG Yong-Chang . Faddeev-Senjanovic Quantization of the Supersymmetrical Electrodynamic System. Chinese Physics C, 2006, 30(12): 1151-1155.
[8]	ZHU Qiao , YANG Zhan-Ying , SHI Kang-Jie , WEN Jun-Qing . Study of Solving a Toda Dynamic System with Loop Algebra. Chinese Physics C, 2006, 30(9): 838-843.
[9]	LIU Wang-Yun , YANG Zhan-Ying , ZHAO Liu . Generalized Toda Mechanics Associated with Classical Lie Algebras D_r. Chinese Physics C, 2004, 28(4): 359-364.
[10]	LIU Bo , GUO Hua . Equation of State for the Thermal System of Nuclear Matter. Chinese Physics C, 2003, 27(7): 590-593.
[11]	YANG ZhanYing , ZHEN Yi . Construction on the Solution of osp(1｜4)Toda Model. Chinese Physics C, 2000, 24(6): 484-489.
[12]	Zhu Yabo , Li Guanglie . A Simple Model Describing the EMC Effect, Nuclear Dr ell-Yan Process, and Inelastic J/ψ Production. Chinese Physics C, 1997, 21(S3): 79-84.
[13]	ZHAO Liu . From Integrability to Conformal Symmetry: Bosonic Superconformal Toda Theories. Chinese Physics C, 1993, 17(5): 431-443.
[14]	ZHAO Liu , YANG Wen-Li . Bosonic Superconformal Toda Model and Dressing Transformation. Chinese Physics C, 1993, 17(4): 338-344.
[15]	Rong Gang , Ma Jimao , Mao Huishun , Wang Tajie , Bai Jingzhi , Li Weiguo . Application of dE/dr Method for e/π Identification of the Measurement of the Mass of τ Heavy Lepton by BES. Chinese Physics C, 1993, 17(S3): 215-224.
[16]	Zhao Liu , Yang Wenli . Bosonic Superconformal Toda Theory and Dressing Symmetry. Chinese Physics C, 1993, 17(S1): 65-72.
[17]	HOU Bo-Yu , ZHAO Liu . Conformally Reduced WZNW Theory,New Extended Chiral Algebras and Their Associated Toda Type Integrable Systems (Ⅱ)An Example. Chinese Physics C, 1993, 17(3): 241-251.
[18]	HOU Bo-Yu , ZHAO Liu . Conformally Reduced WZNW Theory,New Extended Chiral Algebras and Their Associated Toda Type Integrable Systems (Ⅰ) General Framework. Chinese Physics C, 1993, 17(1): 28-37.
[19]	. The Systematical Investigation of Intermittency in High Energy Heavy Ion Collisions. Chinese Physics C, 1991, 15(2): 131-139.
[20]	HOU Bo-Yu , ZHAO Liu , YANG Huan-Xiong . Affine Toda Fields as Restriced WZNW Model. Chinese Physics C, 1991, 15(8): 701-710.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(4525)
PDF Downloads(553)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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.