Article

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

06/1998; DOI:10.1016/S0370-2693(98)00981-2
Source: arXiv

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. Comment: 11 pages, AMSLaTex

0 0
·
0 Bookmarks
·
43 Views
• ##### Conference Proceeding: Low dimensional sigma models
[hide abstract]
ABSTRACT: We discuss classical solutions of U(N) sigma models in two dimensions. We show how from these solutions we can construct solutions of the U(N) sigma model with the Wess--Zumino term (with an arbitrary coefficient). We discuss briefly various properties of these solutions. Next we consider the O(3) sigma model in 2 + 1 dimensions and describe the preliminary results of some numerical work in which we studied the time evolution of some of the previously discussed two dimensional structures (instantons and anti-instantons) under suitable assumptions about their initial values. 9 refs., 6 figs.
12/1987
• Source
##### Article: Ferretti-Rajeev term and homotopy theory
[hide abstract]
ABSTRACT: We reduce Ferretti-Rajeev models to the usual sigma models with Chern-Simons terms (ϑ-terms), and show that whether ϑ is quantized or not corresponds to the fact π4(Gj,n)≅π3(U(j))=ℤ or 0 of the topology in the process of our reduction. We also reconsider the topological invariance of the Chern classes in the language of the field theory.
Communications in Mathematical Physics 01/1994; · 1.97 Impact Factor
• ##### Article: Classical Solutions for the Supersymmetric Grassmannian Sigma Models in Two Dimensions. I
[hide abstract]
ABSTRACT: The supersymmetric version of the complex Grassmannian sigma models (defined on the Grassmann manifold) in two euclidean dimensions is studied. By adopting the newly found solutions of the purely bosonic Grassmannian sigma model as the background fields, we construct explicit fermion classical solutions for the supersymmetric linearized Dirac eqations. These fermion solutions are obtained in an elementary way just like their bosonic partners.
Progress of Theoretical Physics 01/1984; 71(2):388-394. · 2.48 Impact Factor