All generalized SU(2) chiral models have spectral dependent Lax formulation

The equations that define the Lax pairs for generalized principal chiral models can be solved for any nondegenerate bilinear form on su(2). The solution is dependent on one free variable that can serve as the spectral parameter. 1 Formulation of the generalized chiral models Principal chiral models are important example of relativistically invariant field theory integrable by the inverse scattering method. Their Lax pair formulation was given in [1]. Generalized principal chiral models were introduced as a quasiclassical limit of the Baxter quantum XYZ model in [2]. The equations of motion were written in the zero curvature form but without a spectral parameter. The purpose of this paper is to introduce the spectral dependent Lax pair for general SU(2) model. ∗Postal address: Břehová 7, 115 19 Prague 1, Czech Republic. E-mail: [email protected]