The SU(v) Calogero spin system

Kazuhiro Hikami, Miki Wadati

Research output: Contribution to journalArticlepeer-review


A one-dimensional quantum particle system in which particles with su(v) spins interact through inverse square interactions is introduced. We refer to it as the SU(v) Calogero spin system. Using the quantum inverse scattering method, we reveal algebraic structures of the system: hidden symmetry is the U(v) - SU(v) ⊗ U(1) current algebra. This is consistent with the fact that the ground-state wave function is a solution of the Knizhnik-Zamolodchikov equation. Furthermore we show that the system has a higher symmetry, known as the w1 + ∞-algebra. With this W-algebra we have a unified viewpoint on the integrable quantum particle systems with long-range interactions such as the Calogero type ( 1 x2-interactions) and Sutherland type ( 1 sin2x-interactions). The Yangian symmetry is briefly discussed.

Original languageEnglish
Pages (from-to)2509-2526
Number of pages18
JournalChaos, solitons and fractals
Issue number12
Publication statusPublished - Jan 1 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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