Nonlinear Grassmann sigma models in any dimension and an infinite number of conserved currents

Abstract

We first consider nonlinear Grassmann sigma models in any dimension and next construct their submodels. For these models we construct an infinite number of nontrivial conserved currents.Our result is independent of time-space dimensions and, therfore, is a full generalization of that of authors (Alvarez, Ferreira and Guillen).Our result also suggests that our method may be applied to other nonlinear sigma models such as chiral models, G/H sigma models in any dimension. IntroductionNonlinear (Grassmann) sigma models in two dimensions are very interesting objects to study in the not only classical but also quantum point of view and we have a great many papers on this topics. See, for example, Zakrzewski

Submodels of Nonlinear Grassmann Sigma Models in Any Dimension and Conserved Currents, Exact Solutions

“…This is a generalization of ones in previous papers [2], [3], [4], [5]. But, we didn't determine all conserved currents or all exact solutions.…”

“…We review [1] within our necessity. Let M(m, n; C) be the set of m × n matrices over C and M(n; C) be M(n, n; C) for simplicity.…”

“…In [1], for nonlinear Grassmann sigma models in any dimensions, we defined their submodels with both global and local form:…”

A generalization of the submodel of nonlinear models

“…Furthermore, we generalized the definition of submodels to nonlinear Grassmann sigma models and constructed an infinite number of conserved currents and a wide class of exact solutions [6], [7]. (later Ferreira and Leite generalized them to homogeneous-space models [8]).…”

“…Then we calculated an infinite number of conserved currents explicitly in the submodel of nonlinear CP 1 model in (1 + 2)-dimensions [3], [4] (see also [5]). Furthermore, we generalized the definition of submodels to nonlinear Grassmann sigma models and constructed an infinite number of conserved currents and a wide class of exact solutions [6], [7].…”