CP2S Sigma Models Described Through Hypergeometric Orthogonal Polynomials

The main objective of this paper is to establish a new connection between the Hermitian rank-1 projector solutions of the Euclidean C P 2 S sigma model in two dimensions and the particular hypergeometric orthogonal polynomials called Krawtchouk polynomials. We show that any Veronese subsequent analy...

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Bibliographic Details
Published in:Annales Henri Poincaré 2019-10, Vol.20 (10), p.3365-3387
Main Authors: Crampe, N., Grundland, A. M.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Dynamical Systems and Ergodic Theory
Elementary Particles
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
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Summary:The main objective of this paper is to establish a new connection between the Hermitian rank-1 projector solutions of the Euclidean C P 2 S sigma model in two dimensions and the particular hypergeometric orthogonal polynomials called Krawtchouk polynomials. We show that any Veronese subsequent analytical solutions of the C P 2 S 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 C P 2 S models defined using the generalized Weierstrass formula for immersion. We show that these surfaces are homeomorphic to spheres in the su ( 2 s + 1 ) algebra and express several other geometrical characteristics in terms of the Krawtchouk polynomials. Finally, a connection between the su ( 2 ) spin-s representation and the C P 2 S model is explored in detail.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-019-00830-2