2012/12/31 by Alexander Alexandrov, Anton Zabrodin · 1 citation
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP #nlin.SI
paper · pdf · doi:10.1016/j.geomphys.2013.01.007
published as J.Geom.Phys. 67 (2013) 37-80 · 67 pages, 3 figures
arxiv created 2013/09/24 · arxiv updated 2013/09/25
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.