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Regular version of the site

Article

Free fermions and tau-functions

Journal of Geometry and Physics. 2013. Vol. 67. P. 37-80.
Zabrodin A., Alexandrov A.

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.