Free fermions and tau-functions

JOURNAL OF GEOMETRY AND PHYSICS

卷:67

Review

Alexandrov, Alexander^1,2  Zabrodin, Anton^2,3,4 

[1] Univ Freiburg, Inst Math, D-79104 Freiburg, Germany

[2] ITEP, Moscow 117259, Russia

[3] Inst Biochem Phys, Moscow 119991, Russia

[4] Natl Res Univ Higher Sch Econ, Moscow 101000, Russia

关键词: Integrable systems;    Tau-functions;    Free fermions;    Hirota bilinear equations;    Matrix models;   

DOI  :  10.1016/j.geomphys.2013.01.007

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free