Generalized Toda Mechanics Associated with Classical Lie Algebras D<SUB>r</SUB>

LIU Wang-Yun; YANG Zhan-Ying; ZHAO Liu

Chinese Physics C> 2004, Vol. 28> Issue(4) : 359-364

Generalized Toda Mechanics Associated with Classical Lie Algebras D_r

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

Abstract
HTML
Reference
Related

PDF

Abstract：
In this paper, we construct the Lax pair of classical Lie algebra D_r according to the characteristic of its root system, and get a family of integrable generalizations of Toda mechanics (labeled by a pair of ordered integers (m,n), m,n denote the order of positive and negative roots respectively). We aiso provide the explicit equations of motion, the Hamiltonian and the Poission brackets corresponding to the case of m,n≤3.

References

[1]

. Toda M. J. Phys. Soc. Japan, 1967, 22: 431 436; J. Phys. Soc.Japan, 1967, 23: 501-5062. Flaschka H. Phys . Rev. , 1974, B9: 1924 1925; Prog. Theor.Phys. , 1974, 51: 703-7163. Calogero F. J. Math. Phys. , 1971, 12: 419 436; Erratum, 1996,37: 3646; Lett. Nuovo Cimento, 1975, 13: 411-4164. Moser J. Adv. Math. , 1975, 16: 197 220; Prog. in Math. , 8,Birkhauser, Basel, 1980, 233- 2895. Ruijsenaars S N M, Schneider. Ann. Phys. , 1986, 170: 370-4056. Ruijsenaars S N M. Commun. Math. Phys. , 1987, 110: 191-2137. Awat a H, Matsuo Y, Yamamot o T. J. Phys. , 1996, A29: 3089-30988. Brink L et al. Nucl . Phys. , 1993, B401: 591-6129. Bergshoeff E, Vasiliev M. Int . J. Mod. Phys. , 1995, A10: 347710. Marotta V, Sciarrino A. Nucl. Phys. , 1996, B476: 35111. Caracciolo et al. Proceedings of the (Meeting Common Trends in Con..densed Matter and High Energy Physics, Chia Laguna, Cagliari ( Italy,3 10 Sep. 1995) , hep-th/960400912. Felder G. Conformal Field Theory and Integrable Syst ems Associat ed toElliptic Curves, hep-th/940715413. Etingof P I, Kirillov A A. On the Affine Analogs of Jack) s and Mac..donald) s Polynomials, hep-th/940316814. Iso S, Rey S J. Phys. Lett . , 1995, B352: 111-11615. Kawakami N. Phys. Rev. Lett . , 1993, 71: 27516. Azuma H, Iso S. Phys. Lett. , 1994, B331: 10717. Caselle M. Phys. Rev. Lett . , 1995, 74: 277618. Braden H W et al. Nucl . Phys. , 1990, B338: 689; Nucl. Phys. ,1991, B356: 46919. Babelon O, Bernard D. Phys. Lett. , 1993, B317: 36320. Shiota T. J. Math. Phys. , 1995, 35: 584421. Andric I, Bardek V, Jonke L. Phys. Lett . , 1995, B357: 374-37822. Braden H W, Sasaki R. Prog. Theor. Phys. , 1997, 97: 100323. Donagi R, Witten E. Nucl. Phys. , 1996, B460; 299 334, hep-th/951010124. Marshakov A. Seiberg..Witt en Toda Chains and N = 1 SQCD, hep-th/001122225. Marshakov A. Seiberg..Witt en Theory and Integrable Syst ems. WorldScientific Publishing, 199926. Dorey N. An Elliptic Superpotential for Softly Broken N= 4 Supersym..metric Yang..Mills Theory, JHEP 9907, 1999, 021. hep-th/990601127. ZHAO L. Commum. Theor. Phys. , 1993, 15: 22128. HOU Bo..Yu, ZHAO Liu. Int. J. Mod. Phys. , 1993, A8( 6) : 1105-112329. ZHAO Liu, HOU Bo..Yu. Int . J. Mod. Phys. , 1993, A8 ( 21 ) :3773-378930. ZHAO Liu, HOU Bo..Yu. Ann. Phys. , 1994, 230: 1 2031. ZHAO Liu, HOU Bo..Yu. Nucl. Phys. , 1995, B436: 638 65832. WANG Yan..Shen, ZHAO Liu. Sciencia Sinica, 1995, A25: 268 ( inboth Chinese and English)33. YANG Zhan..Yeng, ZHAO Liu, ZHEN Yi. HEP NP, 2000, 24( 2) :9134. YANG Zhan..Yeng, ZHEN Yi. HEP NP, 2000, 24(6) : 48435. ZHAO L, LIU W Y. Higher Toda Mechanics and Spectral Curves, hep-th/030600336. ZHAO L, LIU W Y, YANG Z Y. Generalized Toda Mechanics Associated with Classical Lie Algebras and Their Reductions, hep-th/030608437. Gamboa J et al. Mod. Phys. Lett . , 2001, A16: 2075 2078; hep-th/010422438. Nair V. Phys. Lett . , 2001, B505: 249 254; hep-th/0008027

[1]	Sai Wang , Yi-Fan Wang , Dong-Mei Xia . Constraints on the sum of neutrino masses using cosmological data including the latest extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample. Chinese Physics C, 2018, 42(6): 065103. doi: 10.1088/1674-1137/42/6/065103
[2]	YANG Min , CHEN Hao , MENG Fan-Yong , WEI Dong-Bo . Novel correction method for X-ray beam energy fluctuation of high energy DR system with a linear detector. Chinese Physics C, 2011, 35(11): 1074-1078. doi: 10.1088/1674-1137/35/11/018
[3]	JIANG Yun-Guo , HUANG Yong-Chang . Faddeev-Senjanovic Quantization of the Supersymmetrical Electrodynamic System. Chinese Physics C, 2006, 30(12): 1151-1155.
[4]	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.
[5]	ZHU Qiao , YANG Zhan-Ying , SHI Kang-Ji . The Study on Generalized Toda Mechanics System with Loop Algebra L(D^r). Chinese Physics C, 2005, 29(1): 19-22.
[6]	LIU Bo , GUO Hua . Equation of State for the Thermal System of Nuclear Matter. Chinese Physics C, 2003, 27(7): 590-593.
[7]	YANG ZhanYing , ZHEN Yi . Construction on the Solution of osp(1｜4)Toda Model. Chinese Physics C, 2000, 24(6): 484-489.
[8]	Jie Quanlin , Wang Shunjin , Wei Lianfu . Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure. Chinese Physics C, 1998, 22(2): 111-116.
[9]	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.
[10]	KUANG Le-Man , ZENG Gao-Jian . Super-coherent State Representation of Lie Superalgebra B(0,1). Chinese Physics C, 1993, 17(3): 215-221.
[11]	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.
[12]	ZHAO Liu . From Integrability to Conformal Symmetry: Bosonic Superconformal Toda Theories. Chinese Physics C, 1993, 17(5): 431-443.
[13]	ZHAO Liu , YANG Wen-Li . Bosonic Superconformal Toda Model and Dressing Transformation. Chinese Physics C, 1993, 17(4): 338-344.
[14]	Zhao Liu , Yang Wenli . Bosonic Superconformal Toda Theory and Dressing Symmetry. Chinese Physics C, 1993, 17(S1): 65-72.
[15]	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.
[16]	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.
[17]	HOU Bo-Yu , ZHAO Liu , YANG Huan-Xiong . Affine Toda Fields as Restriced WZNW Model. Chinese Physics C, 1991, 15(8): 701-710.
[18]	SUN Chang-Pu . ON BOSON REALIZATIONS AND INHOMOGENEOUS DIFFERENTIAL REALIZATION FOR LIE ALGEBRAS AND THEIR REPRESENTATIONS. Chinese Physics C, 1990, 14(9): 788-795.
[19]	TU Chuan-Shi . REALIZATION OF THE EMBEDDING OF LIESUBAL GEBRA IN THE CASE OF INTERACTING BOSON MODEL. Chinese Physics C, 1987, 11(5): 634-643.
[20]	HAN QI-ZHI , SONG XING-CHANG , LI GEN-DAO , SUN HONG-ZHOU . IRREDUCIBLE REPRESENTATIONS OF THE GRADED LIE ALGEBRA SU(m/n). Chinese Physics C, 1981, 5(5): 546-553.

Access

Get Citation

LIU Wang-Yun, YANG Zhan-Ying and ZHAO Liu. Generalized Toda Mechanics Associated with Classical Lie Algebras D_r[J]. Chinese Physics C, 2004, 28(4): 359-364.

LIU Wang-Yun, YANG Zhan-Ying and ZHAO Liu. Generalized Toda Mechanics Associated with Classical Lie Algebras D_r[J]. Chinese Physics C, 2004, 28(4): 359-364. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2003-06-25
Revised: 1900-01-01

Article Metric

Article Views(2848)
PDF Downloads(468)
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

Generalized Toda Mechanics Associated with Classical Lie Algebras D_r

Corresponding author: LIU Wang-Yun,

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

Received Date: 2003-06-25

Accepted Date: 1900-01-01

Available Online: 2004-04-05

Abstract: In this paper, we construct the Lax pair of classical Lie algebra D_r according to the characteristic of its root system, and get a family of integrable generalizations of Toda mechanics (labeled by a pair of ordered integers (m,n), m,n denote the order of positive and negative roots respectively). We aiso provide the explicit equations of motion, the Hamiltonian and the Poission brackets corresponding to the case of m,n≤3.

HTML

Reference (1)

Generalized Toda Mechanics Associated with Classical Lie Algebras D_r

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Generalized Toda Mechanics Associated with Classical Lie Algebras D_r

Corresponding author: LIU Wang-Yun,

HTML

目录

Generalized Toda Mechanics Associated with Classical Lie Algebras Dr

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Generalized Toda Mechanics Associated with Classical Lie Algebras Dr

Corresponding author: LIU Wang-Yun,

HTML

目录

Generalized Toda Mechanics Associated with Classical Lie Algebras D_r

Generalized Toda Mechanics Associated with Classical Lie Algebras D_r