2019/09/22 by Nicolas Crampé, Crampé, Nicolas, A. M. Grundland +1
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.1909.10041
The objective of this paper is to establish a new relationship between the\nVeronese subsequent analytic solutions of the Euclidean \ℂP2s\nsigma model in two dimensions and the orthogonal Krawtchouk polynomials. We\nshow that such solutions of the \ℂP2s model, defined on the\nRiemann sphere and having a finite action, can be explicitly parametrised in\nterms of these polynomials. We apply the obtained results to the analysis of\nsurfaces associated with \ℂP2s sigma models, defined using the\ngeneralized Weierstrass formula for immersion. We show that these surfaces are\nspheres immersed in the mathfraksu(2s+1) Lie algebra, and express several\nother geometrical characteristics in terms of the Krawtchouk polynomials.\nFinally, a new connection between the mathfraksu(2) spin-s representation\nand the \ℂP2s model is explored in detail. It is shown that for\nany given holomorphic vector function in \ℂ2s+1 written as a\nVeronese sequence, it is possible to derive subsequent solutions of the\n\ℂP2s model through algebraic recurrence relations which turn out\nto be simpler than the analytic relations known in the literature.\n