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arXiv · hep-th/9301070

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

Kanehisa Takasaki·Takashi Takebe
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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 $\hbar$ 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.)

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Kanehisa Takasaki, Takashi Takebe. 1993-05-24. Quasi-classical limit of Toda hierarchy and W-infinity symmetries. https://doi.org/10.1007/bf00745148

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