Free fermions and tau-functions
Alexander Alexandrov, Anton Zabrodin
TL;DR
This paper reviews the formalism of free fermions in constructing tau-functions for classical integrable hierarchies, detailing their algebraic properties, transformations, and examples with fermionic realizations.
Contribution
It provides a comprehensive derivation of key properties of free fermion formalism and illustrates their application to tau-functions with explicit examples.
Findings
Derivation of group-like properties of normally ordered exponents
Transformation rules between different normal orderings
Explicit fermionic realizations of various tau-functions
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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