Article
Nonlinear Grassmann Sigma Models in Any Dimension and An Infinite Number of Conserved Currents
Waseda University, Edo, Tōkyō, Japan
Physics Letters B (Impact Factor: 6.13). 06/1998; 438(34). DOI: 10.1016/S03702693(98)009812 Source: arXiv
Fulltext preview
arxiv.org Available from: Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

 "From this, we see that [P, ∂ µ P ] are conserved currents (Noether currents). Next, in [1], we defined a submodel of this as simultaneous equations "
[Show abstract] [Hide abstract]
ABSTRACT: In the preceding paper,1 we constructed submodels of nonlinear Grassmann sigma models in any dimensions and, moreover, an infinite number of conserved currents and a wide class of exact solutions. In this letter, we first construct almost all conserved currents for the submodels and all those for CP1model. We next review the Smirnov and Sobolev construction for the equations of CP1submodel and extend the equations, the SS construction and conserved currents to higher order ones. 
 "With P ∈ A θ (R 2+1 ) ⊗ M at(2) we observe that the tensor product [over A θ (R 2+1 )] P ⊗ P is a projector in A θ (R 2+1 ) ⊗ M at(2 2 ). Then the submodel we are interested in may be specified by the equation [43] "
[Show abstract] [Hide abstract]
ABSTRACT: We first review the result that the noncommutative principal chiral model has an infinite tower of conserved currents, and discuss the special case of the noncommutative CP^1 model in some detail. Next, we focus our attention to a submodel of the CP^1 model in the noncommutative spacetime A_\theta(R^2+1). By extending a generalized zero curvature representation to A_\theta(R^2+1) we discuss its integrability and construct its infinitely many conserved currents. Supersymmetric principal chiral model with and without the WZW term and a supersymmetric extension of the CP^1 submodel in noncommutative spacetime (i.e in superspaces A_\theta(R^1+12), A_\theta(R^2+12)) are also examined in detail and their infinitely many conserved currents are given in a systematic manner. Finally, we discuss the solutions of the aforementioned submodels with or without supersymmetry. 
 "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]. (later Ferreira and Leite generalized them to homogeneousspace models [8]). "
[Show abstract] [Hide abstract]
ABSTRACT: We generalize the submodel of nonlinear CP1 models. The generalized models include higher order derivatives. For the systems of higher order equations, we construct a Bäcklundlike transformation of solutions and an infinite number of conserved currents by using the Bell polynomials.