### Abstract

We consider several ternary algebras relevant to physics. We compare and contrast the quantal versions of the algebras, as realized through associative products of operators, with their classical counterparts, as realized through classical Nambu brackets. In some cases involving infinite algebras, we show the classical limit may be obtained by a contraction of the quantal algebra, and then explicitly realized through classical brackets. We illustrate this classical-contraction method by the Virasoro-Witt example.

Original language | English (US) |
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Pages (from-to) | 387-392 |

Number of pages | 6 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 675 |

Issue number | 3-4 |

DOIs | |

State | Published - May 18 2009 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*675*(3-4), 387-392. https://doi.org/10.1016/j.physletb.2009.04.019

**Classical and quantal ternary algebras.** / Curtright, Thomas; Fairlie, David; Jin, Xiang; Mezincescu, Alexandru; Zachos, Cosmas.

Research output: Contribution to journal › Article

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*, vol. 675, no. 3-4, pp. 387-392. https://doi.org/10.1016/j.physletb.2009.04.019

}

TY - JOUR

T1 - Classical and quantal ternary algebras

AU - Curtright, Thomas

AU - Fairlie, David

AU - Jin, Xiang

AU - Mezincescu, Alexandru

AU - Zachos, Cosmas

PY - 2009/5/18

Y1 - 2009/5/18

N2 - We consider several ternary algebras relevant to physics. We compare and contrast the quantal versions of the algebras, as realized through associative products of operators, with their classical counterparts, as realized through classical Nambu brackets. In some cases involving infinite algebras, we show the classical limit may be obtained by a contraction of the quantal algebra, and then explicitly realized through classical brackets. We illustrate this classical-contraction method by the Virasoro-Witt example.

AB - We consider several ternary algebras relevant to physics. We compare and contrast the quantal versions of the algebras, as realized through associative products of operators, with their classical counterparts, as realized through classical Nambu brackets. In some cases involving infinite algebras, we show the classical limit may be obtained by a contraction of the quantal algebra, and then explicitly realized through classical brackets. We illustrate this classical-contraction method by the Virasoro-Witt example.

UR - http://www.scopus.com/inward/record.url?scp=65349099501&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=65349099501&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2009.04.019

DO - 10.1016/j.physletb.2009.04.019

M3 - Article

AN - SCOPUS:65349099501

VL - 675

SP - 387

EP - 392

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 3-4

ER -