Geodesic
Invariant description of $\mathbb{CP}^{N-1}$ sigma models
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 98-111

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We propose an invariant formulation of completely integrable $\mathbb P^{N-1}$ Euclidean sigma models in two dimensions defined on the Riemann sphere $S^2$. We explicitly take the scaling invariance into account by expressing all the equations in terms of projection operators, discussing properties of the operators projecting onto one-dimensional subspaces in detail. We consider surfaces connected with the $\mathbb P^{N-1}$ models and determine invariant recurrence relations, linking the successive projection operators, and also immersion functions of the surfaces.
Keywords: sigma model, projector formalism, invariant recurrence relation.
Mots-clés : soliton surface in a Lie algebra 
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     author = {P. P. Goldstein and A. M. Grundland},
     title = {Invariant description of $\mathbb{CP}^{N-1}$ sigma models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {168},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_168_1_a7/}
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P. P. Goldstein; A. M. Grundland. Invariant description of $\mathbb{CP}^{N-1}$ sigma models. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 98-111. http://geodesic.mathdoc.fr/item/TMF_2011_168_1_a7/