Infinite Number of Integrals of Motion in Classically Integrable System With Boundary (Ⅱ)

Chen Yixin; Luo Xudong

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1998, Vol. 22> Issue(6) : 507-521

Infinite Number of Integrals of Motion in Classically Integrable System With Boundary (Ⅱ)

Chen Yixin ^, ,
Luo Xudong

Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 3100272 Institute of Theoretical Physics, The Chinese Academy of Sciences, Beijing 100080

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Abstract：
In Affine Toda field theory, links among three generating functions for integrals of motion derived from P. (Ⅰ) are studied, and some classically integrable boundary conditions are obtained. An infinite number of integrals of motion are calculated in ZMS model with quasi-periodic condition. We find the classically integrable boundary conditions and K± matrices of ZMS model with independent boundary conditions on each end. It is identified that an infinite number of integrals of motion does exist and one of them is the Hamiltonian, so this system is completely integrable.

References

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Ghoshal S, Zamolodchikov A B. lnt. J. Mod. Phys., 1994. A9:3841-3885 [2] Macintyre A. lntegrable Boundary Conditions for Classical Sine}ordon Theory. Durham Preprint DTP/94-39: heg-th/9410026 [3] Sklyanin E K Funct. Anal. Appl., 1987, 21:164-166; J. Phys., 1988, A21:2375-2389 [4] Bowcock P, Corrigan反Dorey P E et al. Nucl. Phys., 1995, B445:469-500 [5] Chen Yixin, Luo Xudong. Ffigh Energy Phys. and Nucl. Phys. (in Chinese), 1998, 22(5): 413(陈一新，罗旭东.高能物理与核物理，1998,22(5):413) [6] Sasaki R Nucl. Phys，1992, B383:291-305 [7] Mikhailov A V, Olshanetsky M A, Perelomov A M. Commun. Math. Phys., 1981, 79:473 [8] Zamolodchikov A B. Int. J. Mod. Phys., 1988, A3:743-750 [9] Hollwood T. Nucl. Phys., 1992, B384:523-540; Olive D I, Tutok N, Underwood J W R Nucl. Phys.,1993, B401:663-697 [10] Evans J M. Nucl. Phys., 1993, B390:225-250; Zhu Z, Caldi K J. Nucl. Phys., 1995, B436:659-678 [11] Smirnov F A. J. Mod. Phys., 1991; A6:1407-1428; Efthimiou C J. Nucl. Phys., 1993, B398:697-740 [12] Chen Y X, Yang H X, Sheng Z M. Phys. Lett., 1995, B345:149-154 [13] Faddeev L D, Takhtajan A B. Hamitonian Methods in the Theory of Solition. Springer Verlag 1987

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Chen Yixin and Luo Xudong. Infinite Number of Integrals of Motion in Classically Integrable System With Boundary (Ⅱ)[J]. Chinese Physics C, 1998, 22(6): 507-521.

Chen Yixin and Luo Xudong. Infinite Number of Integrals of Motion in Classically Integrable System With Boundary (Ⅱ)[J]. Chinese Physics C, 1998, 22(6): 507-521. shu

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Infinite Number of Integrals of Motion in Classically Integrable System With Boundary (Ⅱ)

Chen Yixin ^,
Luo Xudong

Corresponding author: Chen Yixin,

Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 3100272 Institute of Theoretical Physics, The Chinese Academy of Sciences, Beijing 100080

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1998-06-05

Abstract: In Affine Toda field theory, links among three generating functions for integrals of motion derived from P. (Ⅰ) are studied, and some classically integrable boundary conditions are obtained. An infinite number of integrals of motion are calculated in ZMS model with quasi-periodic condition. We find the classically integrable boundary conditions and K± matrices of ZMS model with independent boundary conditions on each end. It is identified that an infinite number of integrals of motion does exist and one of them is the Hamiltonian, so this system is completely integrable.