### Abstract

Quantum integrable particle systems with inverse square interactions in one-dimensional space are investigated by use of the quantum inverse scattering method. For the case of particles with SU(ν) spins, a hidden symmetry is the SU(ν)U(1)U(ν) current algebra. The system has a higher symmetry, the W1+ algebra. This W algebra structure unifies the Calogero type (1x2 interactions) and the Sutherland type (1sin2x interactions). The energy spectra of the systems are obtained in a simple manner based on the fermion representation of the algebra.

Original language | English |
---|---|

Pages (from-to) | 1191-1194 |

Number of pages | 4 |

Journal | Physical Review Letters |

Volume | 73 |

Issue number | 9 |

DOIs | |

Publication status | Published - Jan 1 1994 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Physical Review Letters*,

*73*(9), 1191-1194. https://doi.org/10.1103/PhysRevLett.73.1191

**Integrable systems with long-range interactions, W algebra, and energy spectrum.** / Hikami, Kazuhiro; Wadati, Miki.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 73, no. 9, pp. 1191-1194. https://doi.org/10.1103/PhysRevLett.73.1191

}

TY - JOUR

T1 - Integrable systems with long-range interactions, W algebra, and energy spectrum

AU - Hikami, Kazuhiro

AU - Wadati, Miki

PY - 1994/1/1

Y1 - 1994/1/1

N2 - Quantum integrable particle systems with inverse square interactions in one-dimensional space are investigated by use of the quantum inverse scattering method. For the case of particles with SU(ν) spins, a hidden symmetry is the SU(ν)U(1)U(ν) current algebra. The system has a higher symmetry, the W1+ algebra. This W algebra structure unifies the Calogero type (1x2 interactions) and the Sutherland type (1sin2x interactions). The energy spectra of the systems are obtained in a simple manner based on the fermion representation of the algebra.

AB - Quantum integrable particle systems with inverse square interactions in one-dimensional space are investigated by use of the quantum inverse scattering method. For the case of particles with SU(ν) spins, a hidden symmetry is the SU(ν)U(1)U(ν) current algebra. The system has a higher symmetry, the W1+ algebra. This W algebra structure unifies the Calogero type (1x2 interactions) and the Sutherland type (1sin2x interactions). The energy spectra of the systems are obtained in a simple manner based on the fermion representation of the algebra.

UR - http://www.scopus.com/inward/record.url?scp=4244151791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4244151791&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.73.1191

DO - 10.1103/PhysRevLett.73.1191

M3 - Article

VL - 73

SP - 1191

EP - 1194

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 9

ER -