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- W2945596411 abstract "The main objective of this paper is to establish a new connection between the Hermitian rank-1 projector solutions of the Euclidean $$mathbb {C}P^{2S}$$ sigma model in two dimensions and the particular hypergeometric orthogonal polynomials called Krawtchouk polynomials. We show that any Veronese subsequent analytical solutions of the $$mathbb {C}P^{2S}$$ model, defined on the Riemann sphere and having a finite action, can be explicitly parametrized in terms of these polynomials. We apply these results to the analysis of surfaces associated with $$mathbb {C}P^{2S}$$ models defined using the generalized Weierstrass formula for immersion. We show that these surfaces are homeomorphic to spheres in the $$mathfrak {su}(2s+1)$$ algebra and express several other geometrical characteristics in terms of the Krawtchouk polynomials. Finally, a connection between the $$mathfrak {su}(2)$$ spin-s representation and the $$mathbb {C}P^{2S}$$ model is explored in detail." @default.
- W2945596411 created "2019-05-29" @default.
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- W2945596411 date "2019-07-30" @default.
- W2945596411 modified "2023-10-09" @default.
- W2945596411 title "$$mathbb {C}P^{2S}$$ Sigma Models Described Through Hypergeometric Orthogonal Polynomials" @default.
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- W2945596411 doi "https://doi.org/10.1007/s00023-019-00830-2" @default.
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