Nonlinear Grassmann Sigma Models in Any Dimension and An Infinite Number of Conserved Currents

TL;DR

This paper demonstrates the existence of an infinite number of conserved currents in nonlinear Grassmann sigma models across any dimension, generalizing previous results and suggesting applicability to other nonlinear sigma models.

Contribution

It constructs an infinite set of conserved currents for Grassmann sigma models in all dimensions, extending prior work and proposing broader applicability.

Findings

Infinite conserved currents in Grassmann sigma models

Dimension-independent conservation laws

Potential extension to other nonlinear sigma models

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.