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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2008 Volume 4, 051, 9 pp. (Mi sigma304)

This article is cited in 6 papers

Quantum Painlevé Equations: from Continuous to Discrete

Hajime Nagoyaa, Basil Grammaticosb, Alfred Ramanic

a Graduate School of Mathematical Sciences, The University of Tokyo, Japan
b IMNC, Université Paris VII \& XI, CNRS, UMR 8165, Bât. 104, 91406 Orsay, France
c Centre de Physique Théorique, Ecole Polytechnique, CNRS, 91128 Palaiseau, France

Abstract: We examine quantum extensions of the continuous Painlevé equations, expressed as systems of first-order differential equations for non-commuting objects. We focus on the Painlevé equations II, IV and V. From their auto-Bäcklund transformations we derive the contiguity relations which we interpret as the quantum analogues of the discrete Painlevé equations.

Keywords: discrete systems; quantization; Painlevé equations.

MSC: 34M55; 37K55; 81S99

Received: March 5, 2008; in final form May 3, 2008; Published online June 9, 2008

Language: English

DOI: 10.3842/SIGMA.2008.051



Bibliographic databases:
ArXiv: 0806.1466


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