Canonical surfaces associated with projectors in Grassmannian sigma models

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3486690· OSTI ID:21476582

Hussin, V ^[1]; Yurdusen, I ^[1]; Zakrzewski, W J ^[2]

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1. Centre de Recherches Mathematiques, Universite de Montreal, C.P. 6128, Succ. Centre-ville, Montreal, Quebec H3C 3J7 (Canada)
2. Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom)

We discuss the construction of higher-dimensional surfaces based on the harmonic maps of S{sup 2} into CP{sup N-1} and other Grassmannians. We show that there are two ways of implementing this procedure - both based on the use of the relevant projectors. We study various properties of such projectors and show that the Gaussian curvature of these surfaces, in general, is not constant. We look in detail at the surfaces corresponding to the Veronese sequence of such maps and show that for all of them this curvature is constant but its value depends on which mapping is used in the construction of the surface.

• OSTI ID: 21476582
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 10; Other Information: DOI: 10.1063/1.3486690; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
AXIOMATIC FIELD THEORY
MAPPING
NONLINEAR PROBLEMS
SIGMA MODEL
SURFACES
TOPOLOGY
BOSON-EXCHANGE MODELS
FIELD THEORIES
MATHEMATICAL MODELS
MATHEMATICS
PARTICLE MODELS
PERIPHERAL MODELS
QUANTUM FIELD THEORY