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(3-4). DOI: 10.1016/S0370-2693(98)00981-2
Source: arXiv


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

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    • "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 "
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    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 CP1-model. We next review the Smirnov and Sobolev construction for the equations of CP1-submodel and extend the equations, the S-S construction and conserved currents to higher order ones.
    Preview · Article · Nov 2011 · Modern Physics Letters A
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    • "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] "
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    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+1|2), A_\theta(R^2+1|2)) 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.
    Preview · Article · May 2008 · Physical Review D
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    • "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 homogeneous-space models [8]). "
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    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 Bäcklund-like transformation of solutions and an infinite number of conserved currents by using the Bell polynomials.
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