Free fermions and tau-functions

Alexander Alexandrov, Anton Zabrodin

Research output: Contribution to journalReview articlepeer-review

47 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)37-80
Number of pages44
JournalJournal of Geometry and Physics
Publication statusPublished - May 2013
Externally publishedYes


  • Free fermions
  • Hirota bilinear equations
  • Integrable systems
  • Matrix models
  • Tau-functions


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