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TMF, 2011, Volume 168, Number 1, Pages 98–111 (Mi tmf6666)  

This article is cited in 3 scientific papers (total in 3 papers)

Invariant description of $\mathbb{CP}^{N-1}$ sigma models

P. P. Goldsteina, A. M. Grundlandbc

a Theoretical Physics Department, The Andrzej Soltan Institute for Nuclear Studies, Warsaw, Poland
b Centre de Recherches Mathématiques, Université de Montréal, Montréal, Canada
c Université du Québec à Trois-Rivières, Canada

Abstract: 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, soliton surface in a Lie algebra, projector formalism, invariant recurrence relation

DOI: https://doi.org/10.4213/tmf6666

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English version:
Theoretical and Mathematical Physics, 2011, 168:1, 939–950

Bibliographic databases:

Document Type: Article

Citation: P. P. Goldstein, A. M. Grundland, “Invariant description of $\mathbb{CP}^{N-1}$ sigma models”, TMF, 168:1 (2011), 98–111; Theoret. and Math. Phys., 168:1 (2011), 939–950

Citation in format AMSBIB
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\pages 98--111
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Goldstein P.P., Grundland A.M., Post S., “Soliton surfaces associated with sigma models: differential and algebraic aspects”, J. Phys. A, 45:39 (2012), 395208, 19 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    2. Dey S., Grundland A.M., “Properties of Soliton Surfaces Associated With Integrable SIGMA Models”, J. Phys. A-Math. Theor., 50:33 (2017), 335201  crossref  zmath  isi  scopus
    3. Goldstein P.P., Grundland A.M., “On a Stack of Surfaces Obtained From the Cpn-1 SIGMA Models”, J. Phys. A-Math. Theor., 51:9 (2018), 095201  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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