Fredholm determinants and the mKdV/Sinh-Gordon hierarchies

1995/06/30 by Craig A. Tracy, Harold Widom · 4 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.MP #nlin.SI #solv-int

paper · pdf · doi:10.1007/bf02103713

published as Commun. Math. Phys 179 (1996) 1--9 · 11 pages, LaTeX file, no figures

arxiv created 1995/07/07 · openalex publication_date 1996/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For a particular class of integral operators K we show that the quantity \ph:=log det (I+K)-log det (I-K) satisfies both the integrated mKdV hierarchy and the sinh-Gordon hierarchy. This proves a conjecture of Zamolodchikov.

Citations

• Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region
• Fredholm determinants, differential equations and matrix models

Cited by

• The determinant representation for quantum correlation functions of the sinh-Gordon model
• Fredholm Determinants and Pole-free Solutions to the Noncommutative Painlevé II Equation
• Backlund transformation for integrable hierarchies: example - mKdV hierarchy
• The complex sine-Gordon equation as a symmetry flow of the AKNS hierarchy