Supersymmetric sigma-model as Gross-Neve model

I will show that there is a wide class of integrable sigma models (including, for example, the CP^n model) equivalent to the Gross-Neveu bosonic models. Within the framework of this approach, a consistent method has been developed for describing models with fermions, including supersymmetric ones, in terms of supersymplectic factors. I will also talk about the calculation of the beta function of such theories in higher loops, as well as, if time permits, about some applications in quantum mechanics.