Baxter Q-operators in Ruijsenaars-Sutherland hyperbolic systems: one- and two-particle cases
N. Belousov, S. Derkachov, S. Kharchev, S. Khoroshkin
TL;DR
This paper reviews the use of Baxter Q-operators in Ruijsenaars-Sutherland hyperbolic systems for one and two particles, demonstrating dual integral representations and establishing orthogonality and completeness of eigenfunctions.
Contribution
It introduces the application of Baxter Q-operators to hyperbolic systems with explicit proofs of eigenfunction properties for one- and two-particle cases.
Findings
Eigenfunctions have dual integral representations
Orthogonality and completeness are proven
Q-operators facilitate analysis of hyperbolic systems
Abstract
In these notes we review the technique of Baxter Q-operators in the Ruijsenaars-Sutherland hyperbolic systems in the cases of one and two particles. Using these operators we show in particular that eigenfunctions of these systems admit two dual integral representations and prove their orthogonality and completeness.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models