The Lax pair by dimensional reduction of Chern–Simons gauge theory

DOI10.1063/1.531636zbMath0863.58040arXivhep-th/9511184OpenAlexW3099562746MaRDI QIDQ5284866

Oktay K. Pashaev

Publication date: 3 June 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9511184

zbMATH Keywords

nonlinear Schrödinger equationsolitonsLax pairChern-Simons topological gauge theory

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Yang-Mills and other gauge theories in quantum field theory (81T13) NLS equations (nonlinear Schrödinger equations) (35Q55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Soliton equations (35Q51)

Related Items

GRAVITY-ASSISTED SOLUTION OF THE MASS GAP PROBLEM FOR PURE YANG–MILLS FIELDS ⋮ REDUCTIONS OF CHERN–SIMONS THEORY RELATED TO INTEGRABLE SYSTEMS WHICH HAVE GEOMETRIC APPLICATIONS ⋮ Integrable models as constrained topological gauge theory ⋮ AN INTEGRABLE MODEL WITH SOLITON SOLUTIONS WHICH HAVE APPLICATIONS TO TWO-DIMENSIONAL GRAVITY ⋮ Moving frames hierarchy and BF theory ⋮ Pontrjagin forms, Chern Simons classes, Codazzi transformations, and affine hypersurfaces

Cites Work

• Topological quantum field theory
• Quantum field theory and the Jones polynomial
• A self-dual Yang-Mills hierarchy and its reductions to integrable systems in \(1+1\) and \(2+1\) dimensions
• Classical symmetries of some two-dimensional models
• Topological gauge theories of antisymmetric tensor fields
• Bilinearization of multidimensional topological magnets
• Lineal gravity from planar gravity