Free fermions and tau-functions |
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| Institution: | 1. Mathematisches Institut, Albert-Ludwigs-Universität, Freiburg 79104, Germany;2. ITEP, 25 Bol. Cheremushkinskaya Ulitsa, Moscow 117259, Russia;3. Institute of Biochemical Physics, 4 Kosygina Ulitsa, Moscow 119991, Russia;4. National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, Moscow 101000, Russia |
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| Abstract: | 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. |
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