Publication: Scaling self-similar formulation of the string equations of the hermitian one-matrix model
Loading...
Official URL
Full text at PDC
Publication Date
1993-11-11
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier Science BV
Citations
Exportar
Abstract
The string equation appearing in the double scaling limit of the Hermitian one–matrix model, which corresponds to a Galilean self–similar condition for the KdV hierarchy, is reformulated as a scaling self–similar condition for the Ur–KdV hierarchy. A non– scaling limit analysis of the one–matrix model has led to the complexified NLS hierarchy and a string equation. We show that this corresponds to the Galilean self– similarity condition for the AKNS hierarchy and also its equivalence to a scaling self– similar condition for the Heisenberg ferromagnet hierarchy.
Description
©Elsevier Science BV.
UCM subjects
Unesco subjects
Keywords
Citation
[1] M.Adler and J.Moser, Commun.Math.Phys. 61 (1978) 1.
[2] E.Brezin and V.Kazakov, Phys.Lett. 236B (1990) 144; M.Douglas and M.Shenker, Nucl.Phys. B335 (1990) 685; D.Gross and A.Migdal, Phys.Rev.Lett. 64 (1990) 127.
[3] L.Bonora and C.Xiong, Phys.Lett. 285B (1992) 191; Matrix models without scaling limit Int.J.Mod.Phys. A (1993) to appear.
[4] S.Dalley, C.Johnson, and T.Morris, Nuc.Phys. B368 (1992) 625, 655; S.Dalley, preprint PUPT, 1290 (1991); C.Johnson, T.Morris, and Wätterstam, Phys.Lett. 291B (1992) 11; C.Johnson, T.Morris, and P.White, Phys.Lett. 292B (1992) 283; S.Dalley, C.Johnson, T.Morris, and A.Wättersman, Mod.Phys.Lett. A29 (1992) 2753; A.Wättersman, Phys.Lett. 263B (1991) 51.
[5] L.Faddeev and L.Takhtajan, Hamiltonian Methods in the Theory of Solitons Springer Verlag (1987), Berlin.
[6] A.Forsyth, Theory of Functions of Complex Variable Cambridge University Press (1893), Cambridge.
[7] I.Gel’fand and L.Dickii, Russ.Math.Surv. 30 (1975) 67; Func.Anal.Appl. 13 (1979) 6.
[8] F.Guil and M.Mañas, Phys.Lett. 153A (1991) 90.
[9] F.Guil and M.Mañas, Self–similarity in the KdV hierarchy. Geometry of the string equations in Nonlinear Evolution Equations and Dynamical Systems’92 edited by V.Mahankov, O.Pashaev, and I.Puzynin, World Scientific (1992), Singapure; Strings equations for the KdV hierarchy and the Grassmannian J.Phys.A: Math. & Gen. (1993), to appear.
[10] V.Kac and A.Schwarz, Phys.Lett. 257B (1991) 329.
[11] I.Krichever and S.Novikov, Russ.Math.Surv. 35 (1980) 53.
[12] H.La, Mod.Phys.Lett.A 6 (1991) 573; Commun.Math.Phys. 140 (1991) 569.
[13] I.McIntosh, Proc.Roy.Soc. Edinburgh 115A (1990) 367.
[14] W.Magnus, F.Oberhettinger, and R.Soni, Formulas and Theorems for the Special Functions of Mathematical Physics Springer Verlag (1966), Berlin.
[15] M.Mañas and P.Guha, String equations for the unitary matrix model and the periodic flag manifold (1993) to appear.
[16] S.Svinolupov and V.Sokolov, Func.Anal.Appl. 16 (1983) 317; S.Svinolupov, V.Sokolov, and R.Yamilov, Sov.Math.Dokl. 28 (1983) 165.
[17] G.Wilson, Phys.Lett. 132A (1989) 445.
[18] E.Witten, Surv.Diff.Geom. 1 (1991) 243; M.Kontsevich, Commun.Math.Phys. 147 (1992) 1.