期刊
JOURNAL OF GEOMETRY AND PHYSICS
卷 67, 期 -, 页码 37-80出版社
ELSEVIER
DOI: 10.1016/j.geomphys.2013.01.007
关键词
Integrable systems; Tau-functions; Free fermions; Hirota bilinear equations; Matrix models
资金
- Ministry of Education and Science of Russian Federation [8207]
- RFBR grant [11-01-00962, 11-02-01220, 12-02-91052-CNRS, 12-02-92108-JSPS]
- ERC Starting Independent Researcher Grant StG [204757-TQFT]
- [NSh-3349.2012.2]
We review the formalism of free fermions used for construction of tau-functions of classical integrable hierarchies and give a detailed derivation of group-like properties of the normally ordered exponents, transformations between different normal orderings, the bilinear relations, the generalized Wick theorem and the bosonization rules. We also consider various examples of tau-functions and give their fermionic realization. (C) 2013 Elsevier B.V. All rights reserved.
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