Sine-Gordon quantum field theory on the half-line with quantum boundary degrees of freedom

2002/08/31 by Pascal Baseilhac, P. Baseilhac, Kozo Koizumi +1 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bound state #Boundary (topology) #Boundary conformal field theory #Boundary value problem #Coupling constant #Mathematical analysis #Mathematical physics #Mathematics #Neumann boundary condition #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantization (signal processing) #Quantum #Quantum field theory #Quantum mechanics #Robin boundary condition #S-matrix #Soliton #cond-mat #hep-th #math-ph #math.MP #nlin.SI #sine-Gordon equation

paper · pdf · doi:10.1016/s0550-3213(02)00980-x

published as Nucl.Phys.B649:491-510,2003 · 15 pages, LaTeX file with amssymb, v2: references added, Comments added, typos corrected. To appear in Nucl.Phys. B

arxiv created 2002/11/02 · openalex publication_date 2002/12/30 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The sine-Gordon model on the half-line with a dynamical boundary introduced by Delius and one of the authors is considered at quantum level. Classical boundary conditions associated with classical integrability are shown to be preserved at quantum level too. Non-local conserved charges are constructed explicitly in terms of the field and boundary operators. We solve the intertwining equation associated with a certain coideal subalgebra of U_q(sl₂) generated by these non-local charges. The corresponding solution is shown to satisfy quantum boundary Yang-Baxter equations. Up to an exact relation between the quantization length of the boundary quantum mechanical system and the sine-Gordon coupling constant, we conjecture the soliton/antisoliton reflection matrix and boundstates reflection matrices. The structure of the boundary state is then considered, and shown to be divided in two sectors. Also, depending on the sine-Gordon coupling constant a finite set of boundary bound states are identified. Taking the analytic continuation of the coupling, the corresponding boundary sinh-Gordon model is briefly discussed. In particular, the particle reflection factor enjoys weak-strong coupling duality.

Citations

• New boundary conditions for integrable lattices
• Generalisations of the Coleman-Thun mechanism and boundary reflection factors
• Solitons in affine Toda field theories
• Boundary conditions for integrable quantum systems
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

Cited by

• Classification of reflection matrices related to (super-)Yangians and application to open spin chain models
• A new (in)finite-dimensional algebra for quantum integrable models
• On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary