Invariant formulation of surfaces associated with CP^N-1 models

2010/02/15 by P. P. Goldstein, Goldstein, P. P., A. M. Grundland +1
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #53A07 #53B50 #53C43 #81T45 #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Seismic Imaging and Inversion Techniques #math-ph #math.MP #msc:53A07 #msc:53B50 #msc:53C43 #msc:81T45 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1002.2906

15 pages

arxiv created 2010/02/15 · openalex publication_date 2010/02/15 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we provide an invariant formulation of completely integrable CP^N-1 Euclidean sigma models in two dimensions defined on the Riemann sphere S². The scaling invariance is explicitly taken into account by expressing all the equations in terms of projection operators. Properties of the projectors mapping onto one-dimensional subspaces are discussed in detail. The paper includes a discussion of surfaces connected with the CP^N-1 models and the wave functions of their linear spectral problem.

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