Free fermions and tau-functions

Alexander Alexandrov, Anton Zabrodin

Published 2012-12-25, updated 2013-09-24Version 3

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.