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The objective of this paper is to establish a new relationship between the Veronese subsequent analytic solutions of the Euclidean $\mathbb{C}P^{2s}$ sigma model in two dimensions and the orthogonal Krawtchouk polynomials. We show that such…

Mathematical Physics · Physics 2019-09-24 Nicolas Crampé , Alfred Michel Grundland

In this paper, we study rank-1 projector solutions to the completely integrable Euclidean $CP^{N-1}$ sigma model in two dimension and their associated surfaces immersed in the $su(N)$ Lie algebra. We reinterpret and generalize the proof of…

Analysis of PDEs · Mathematics 2010-10-12 S. Post , A. M. Grundland

We investigate certain properties of $\mathfrak{su}(N)$-valued two-dimensional soliton surfaces associated with the integrable $\mathbb{C}P^{N-1}$ sigma models constructed by the orthogonal rank-one Hermitian projectors, which are defined…

Mathematical Physics · Physics 2017-07-21 Sanjib Dey , A. M. Grundland

We establish and analyze a new relationship between the matrices describing an arbitrary component of a spin $s$, where $2s\in \mathbb{Z}^+$, and the matrices of $\mathbb{C}P^{2s}$ two-dimensional Euclidean sigma models. The spin matrices…

Mathematical Physics · Physics 2020-05-05 P. P. Goldstein , A. M. Grundland , A. M. Escobar Ruiz

In this paper, the Weierstrass technique for harmonic maps S^2 -> CP^(N-1) is employed in order to obtain surfaces immersed in multidimensional Euclidean spaces. It is shown that if the CP^(N-1) model equations are defined on the sphere S^2…

Differential Geometry · Mathematics 2015-05-13 A. M. Grundland , I. Yurdusen

We study analytic descriptions of conformal immersions of the Riemann sphere S^2 into the CP^(N-1) sigma model. In particular, an explicit expression for two-dimensional (2-D) surfaces, obtained from the generalized Weierstrass formula, is…

Differential Geometry · Mathematics 2015-05-13 A. M. Grundland , I. Yurdusen

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 $S^2$. The scaling invariance is explicitly taken into account by expressing all…

Mathematical Physics · Physics 2010-02-16 P. P. Goldstein , A. M. Grundland

Two-dimensional conformally parametrized surfaces immersed in the su(N) algebra are investigated. The focus is on surfaces parametrized by solutions of the equations for the CP^(N-1) sigma model. The Lie-point symmetries of the CP^(N-1)…

Differential Geometry · Mathematics 2009-11-13 A. M. Grundland , W. A. Hereman , I. Yurdusen

In this paper we present results obtained from the unification of $SU(2)$ coherent states with $\mathbb{C}P^N$ sigma models defined on the Riemann sphere having finite actions. The set of coherent states generated by a vector belonging to a…

Mathematical Physics · Physics 2017-07-31 A. M. Grundland , A. Strasburger , D. Dziewa-Dawidczyk

In this paper, we consider both differential and algebraic properties of surfaces associated with sigma models. It is shown that surfaces defined by the generalized Weierstrass formula for immersion for solutions of the CP^{N-1} sigma model…

Mathematical Physics · Physics 2015-06-05 P. P. Goldstein , A. M. Grundland , S. Post

An extension of the classic Enneper-Weierstrass representation for conformally parametrised surfaces in multi-dimensional spaces is presented. This is based on low dimensional CP^1 and CP^2 sigma models which allow the study of the constant…

Dynamical Systems · Mathematics 2015-06-26 A. M. Grundland , W. J. Zakrzewski

We study certain new properties of 2D surfaces associated with the $\mathbb{C}P^{N-1}$ models and the wave functions of the corresponding linear spectral problem. We show that $su(N)$-valued immersion functions expressed in terms of rank-1…

Exactly Solvable and Integrable Systems · Physics 2011-04-08 P. P. Goldstein , A. M. Grundland

In this paper, we present invariant recurrence relations for the completely integrable CP^(N-1) Euclidean sigma model in two dimensions defined on the Riemann sphere S^2 when its action functional is finite. We determine the links between…

Mathematical Physics · Physics 2014-11-20 P. Goldstein , A. M. Grundland

Under the assumption that the $\mathbb{C}P^{N-1}$ sigma model is defined on the Riemann sphere and its action functional is finite, we derive surfaces induced by surfaces and we demonstrate that the stacked surfaces coincide with each…

Mathematical Physics · Physics 2018-03-14 P P Goldstein , A M Grundland

We study some geometrical aspects of two dimensional orientable surfaces arrising from the study of CP^N sigma models. To this aim we employ an identification of R^(N(N+2)) with the Lie algebra su(N+1) by means of which we construct a…

Differential Geometry · Mathematics 2009-11-11 A. M. Grundland , A. Strasburger , W. J. Zakrzewski

We present a unified method of construction of surfaces associated with Grassmannian sigma models, expressed in terms of an orthogonal projector. This description leads to compact formulae for structural equations of two-dimensional…

Differential Geometry · Mathematics 2007-05-23 A. M. Grundland , L. Snobl

This paper is devoted to a study of the connection between the immersion functions of two-dimensional surfaces in Euclidean or hyperbolic spaces and classical orthogonal polynomials. After a brief description of the soliton surfaces…

Mathematical Physics · Physics 2019-12-24 Vincent Chalifour , Alfred Michel Grundland

The sigma model on complex projective superspaces CP^{S-1|S} gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle \theta. Our main goal is to…

High Energy Physics - Theory · Physics 2010-02-11 Constantin Candu , Vladimir Mitev , Thomas Quella , Hubert Saleur , Volker Schomerus

The objective of this paper is to construct and investigate smooth orientable surfaces in $R^{N^2-1}$ by analytical methods. The structural equations of surfaces in connection with $CP^{N-1}$ sigma models on Minkowski space are studied in…

Differential Geometry · Mathematics 2007-05-23 A. M. Grundland , L. Snobl

A superintegrable finite model of the quantum isotropic oscillator in two dimensions is introduced. It is defined on a uniform lattice of triangular shape. The constants of the motion for the model form an SU(2) symmetry algebra. It is…

Mathematical Physics · Physics 2015-06-11 Hiroshi Miki , Sarah Post , Luc Vinet , Alexei Zhedanov
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