Lax pair and Darboux transformation of a noncommutativeU(N) principal chiral model

2006/08/29 by U. Saleem, M. Hassan, Mahmood Ul Hassan
Chemistry · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Chemistry #Chiral model #Formalism (music) #Generalization #Integrable system #Lax pair #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Parametric statistics #Pure mathematics #Transformation (genetics) #hep-th

paper · pdf · doi:10.1088/0305-4470/39/37/021

published as J.Phys.A39:11683-11696,2006 · 1+20 pages

openalex publication_date 2006/08/29 · arxiv created 2006/09/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

We present a noncommutative generalization of the Lax formalism of the U ( N ) principal chiral model in terms of a one-parameter family of flat connections. The Lax formalism is further used to derive a set of parametric noncommutative Bäcklund transformations and an infinite set of conserved quantities. From the Lax pair, we derive a noncommutative version of the Darboux transformation of the model.

Citations

• String theory and noncommutative geometry
• Zero-curvature formalism of supersymmetric principal chiral model
• Restrictions on gauge groups in noncommutative gauge theory
• Noncommutative multi-solitons in 2+1 dimensions
• Towards noncommutative integrable systems
• Soliton-Antisoliton Scattering Configurations in a Noncommutative Sigma Model in 2+1 Dimensions
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
• Quantum mechanics as a statistical theory