Quasi-classical limit of Toda hierarchy and W-infinity symmetries

Abstract

Previous results on quasi-classical limit of the KP hierarchy and its W-infinity symmetries are extended to the Toda hierarchy. The Planck constant $\hslash$ now emerges as the spacing unit of difference operators in the Lax formalism. Basic notions, such as dressing operators, Baker-Akhiezer functions and tau function, are redefined. $W_{1+\infty }$ symmetries of the Toda hierarchy are realized by suitable rescaling of the Date-Jimbo-Kashiara-Miwa vertex operators. These symmetries are contracted to $w_{1+\infty }$ symmetries of the dispersionless hierarchy through their action on the tau function. (A few errors in the earlier version is corrected.)

14 pages, Kyoto University KUCP-0057/93

References in corpus (2)

• SDiff(2) Toda equation -- hierarchy, $\tau$ function, and symmetries
• Interacting Theory of Collective and Topological Fields in 2 Dimensions

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