The master T-operator for the Gaudin model and the KP hierarchy

2013/06/30 by A. Alexandrov, Alexander Alexandrov, Sebastien Leurent +4 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Bilinear interpolation #Boundary value problem #Computer science #Connection (principal bundle) #Construct (python library) #Eigenvalues and eigenvectors #Geometry #Hierarchy #Law #Master equation #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Physics #Pure mathematics #Quantum #Quantum mechanics #Statistics #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1016/j.nuclphysb.2014.03.008

published as Nucl. Phys. B 883 (2014) 173-223 · 56 pages, v2: details added in appendix C, v3: published version

openalex publication_date 2014/03/25 · arxiv created 2014/04/14 · arxiv updated 2014/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Following the approach of [1], we construct the master T-operator for the quantum Gaudin model with twisted boundary conditions and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. We also characterize the class of solutions to the KP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum Gaudin model and the classical Calogero–Moser system of particles.

Citations

• Classical tau-function for quantum spin chains
• Solitons and Infinite Dimensional Lie Algebras
• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• Diagonalisation d'une classe d'hamiltoniens de spin
• Gaudin model, Bethe Ansatz and critical level
• Bethe ansatz and Hirota equation in integrable models

Cited by

• Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary
• Self-Duality and Scattering Map for the Hyperbolic van Diejen Systems with Two Coupling Parameters (with an Appendix by S. Ruijsenaars)
• The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy