P. P. Goldstein, A. M. Grundland, “Invariant description of <nobr>$\mathbb{CP}^{N-1}$</nobr> sigma models”, TMF, 2011, Volume 168, Number 1,Pages <nobr>98

This article is cited in 4 papers

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

P. P. Goldstein^a, A. M. Grundland^bc

^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: 10.4213/tmf6666