Abstract
The Krichever-Novikov bases are studied on Riemann surfaces with more-than-two punctures. The bases are presented and the completness theorem is proven for the case of integer (up to a common constant) momenta. Then the interacting strings are considered, the amplitudes and partition functions are obtained, comparable with that of path-integral approach. For the amplitudes the simple geometric implication is proposed.
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Krichever, I.M., Novikov, S.P.: Virasoro-type algebras, Riemann surfaces and structures of the soliton theory. Func. Anal. Pril.1, 46–63 (1987)
Krichever, I.M., Novikov, S.P.: Virasoro-type algebras, Riemann surfaces and string in Minkovski space. Func. Anal. Pril.214, 47–61 (1987)
Krichever, I.M., Novikov, S.P.: Virasoro-type algebras, pseudo-tensor of energy-momentum and operator expansions on the Riemann surfaces. Func. Anal. Pril.231 (1989)
Krichever, I.M., Novikov, S.P.: Riemann surfaces, operator fields, strings. Analogues of the Fourier-Laurent bases. Preprint IHES/P/89/26 (April 1989)
Krichever, I.M.: Spectral theory of two-dimensional periodic operators and its applications. Uspec. Mat. Nauk.442, 121–183 (1989)
Krichever, I.M.: The algebraic curves and the nonlinear equations. Uspec. Mat. Nauk.334, 215–216 (1978)
Polyakov, A.M.: Phys. Lett.13, 207 (1981); Belavin, A., Knizhnik, V.: Phys. Lett.168 B, 201 (1986); Morozov, A.Yu.: Phys. Lett.184 B, 171 (1987)
Dick, R.: Lett. Math. Phys.18, 255 (1989); Dick, R.: Holomorphic differentials on Punctured Riemann surfaces. Preprint DESY 89-097 (August 1989)
Schlichenmaier, M.: Central extensions and semi-infinite wedge representations of Krichever-Novikov algebras for more than two points. Preprint Manusk. Fak. Math u. Inf. Mannheim 102–1989 (September 1989)
Jaffe, A., Klimek, S., Lesniewski, A.: Representations of the Heisenberg algebra on a Riemann surface. Preprint HUTMP 89/B239 (April 1989)
Venetziano, S.: An introduction to dual models. Phys. Rep.9, 199 (1974)
Green, M.B., Schwarz, J.H., Witten, E.: Superstring theory I, II. Cambridge: Cambridge University Press 1987
Fay, J.: Theta functions on Riemann surfaces. Lecture Notes in Mathematics, vol. 352. Berlin, Heidelberg, New York: Springer 1973
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Communicated by Ya. G. Sinai
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Sadov, V.A. Bases on multipunctured Riemann surfaces and interacting strings amplitudes. Commun.Math. Phys. 136, 585–597 (1991). https://doi.org/10.1007/BF02099075
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DOI: https://doi.org/10.1007/BF02099075