Classically integrable boundary conditions for symmetric-space sigma models

摘要

We investigate boundary conditions for the non-linear sigma model on the compact symmetric space G/H. The Poisson brackets and the classical local conserved charges necessary for integrability are preserved by boundary conditions which correspond to involutions which commute with the involution defining H. Applied to SO(3)/SO(2), the non-linear sigma model on S-2, these yield the great circles as boundary submanifolds. Applied to G x G/G, they reproduce known results for the principal chiral model. (C) 2004 Elsevier B.V. All rights reserved.