Integrability of Liouville System on High Genus Riemann Surface.Ⅰ. Classical Case

CHEN Yi-Xin; GAO Hong-Bo

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2024年10月30日

Chinese Physics C> 1992, Vol. 16> Issue(4) : 323-334

Integrability of Liouville System on High Genus Riemann Surface.Ⅰ. Classical Case

CHEN Yi-Xin ^, ,
GAO Hong-Bo

Zhejiang Institute of Modern Physics,Zhejiang University,Hangzhou 310027

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Abstract：
By using the theory of uniformization of Riemann surfaces,we study properties of the Liouville equation and its general solution on a Riemann surface of genus g>1.After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices,we prove the classical integrability of Liouville system on high genus Riemann surface.

References

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A. M. Polyakov, Mod. Phys, Lett., A2(1987), 893;V. G. Knizhnik, A. M. Polyakov and A. B. Zamolodchikov, Mod. Phys. Lett., A3(1988), 819,[2] J.-L. Gervais, preprint LPTENS 89/14;F. Smirnov and L. Takhtajan, preprint PAMUC 90/12.[3] O. Babelon and C. M. Viallet, preprint SISSA-89-54;E. Cremmer and J.-L. Gervais, Commun. Math. Phys. 134(1990), 619.[4] V. G. Drinfeld, proc. ICM-86, Berkeley, 1(1986), 798;M. Jimbo, Lett. Math. Phys., 10(1985), 63.[5] D. Friedan and S. Shenker, Nucl. Phys,, B281(1987), 509;T. Eguchi and H. Ooguri, Nucl. Phys., B282(1987), 308.[6] D. Gross and A. Migdal, Nucl. Phys., B340(1990), 333.[7] P. G. Zograf and L. A. Takhtajan, Math. USSR Sborrsik, 132(1987), 147.[8] A. F. Beardon,《离散群几何》(中译本)北京理工大学出版社(1988),[9] L. D. Faddeev and L. A. Takhtajan, Lect: Notes in Phys., 246(1986), 166;A. K. Pogrebkov and M. K. Polivanov, Soviet Sci. Rev., C3(1985), 198.[10] L. D. Faddeev, Commun. Math. Phys., 132(1990), 139.[11] N. S. Hawley and M. Schiffer, ,Acta Math，115(1966), 199.

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CHEN Yi-Xin and GAO Hong-Bo. Integrability of Liouville System on High Genus Riemann Surface.Ⅰ. Classical Case[J]. Chinese Physics C, 1992, 16(4): 323-334.

CHEN Yi-Xin and GAO Hong-Bo. Integrability of Liouville System on High Genus Riemann Surface.Ⅰ. Classical Case[J]. Chinese Physics C, 1992, 16(4): 323-334. shu

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

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Integrability of Liouville System on High Genus Riemann Surface.Ⅰ. Classical Case

CHEN Yi-Xin ^,
GAO Hong-Bo

Corresponding author: CHEN Yi-Xin,

Zhejiang Institute of Modern Physics,Zhejiang University,Hangzhou 310027

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1992-04-05

Abstract: By using the theory of uniformization of Riemann surfaces,we study properties of the Liouville equation and its general solution on a Riemann surface of genus g>1.After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices,we prove the classical integrability of Liouville system on high genus Riemann surface.