2016/07/22 by Steven T. Haworth, Haworth, Steven, S. N. M. Ruijsenaars +1
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1607.06675
openalex publication_date 2016/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present and study a novel class of one-dimensional Hilbert space\neigenfunction transforms that diagonalize analytic difference operators\nencoding the (reduced) two-particle relativistic hyperbolic Calogero-Moser\ndynamics. The scattering is described by reflection and transmission amplitudes\nt and r with function-theoretic features that are quite different from\nnonrelativistic amplitudes. The axiomatic Hilbert space analysis in the\nappendices is inspired by and applied to the attractive two-particle\nrelativistic Calogero-Moser dynamics for a sequence of special couplings.\nTogether with the scattering function u of the repulsive case, this leads to\na triple of amplitudes u, t, r satisfying the Yang-Baxter equations.\n