Fermionic construction of the partition function for multimatrix models and the multicomponent Toda lattice hierarchy |
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| Authors: | J Harnad A Yu Orlov |
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| Institution: | (1) Centre de Recherches Mathématiques, Université de Montréal, C. P. 6128, Succ. Centre Ville, Montréal, Québec, Canada, H3C 3J7;(2) Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke W., Montréal, Qué bec, Canada, H4B 1R6;(3) Nonlinear Wave Processes Laboratory, Shirshov Institute of Oceanology, RAS, Moscow, Russia |
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| Abstract: | We use p-component fermions, p = 2, 3,..., to represent (2p−2)N-fold integrals as a fermionic vacuum expectation. This yields
a fermionic representation for various (2p−2)-matrix models. We discuss links with the p-component Kadomtsev-Petviashvili
hierarchy and also with the p-component Toda lattice hierarchy. We show that the set of all but two flows of the p-component
Toda lattice hierarchy changes standard matrix models to new ones.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 265–277, August, 2007. |
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| Keywords: | matrix model tau function of multicomponent Toda chain integrable system |
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