Classical and quantal ternary algebras

Thomas Curtright; David Fairlie; Xiang Jin; Luca Mezincescu; Cosmas Zachos

doi:10.1016/j.physletb.2009.04.019

Classical and quantal ternary algebras

Thomas Curtright, David Fairlie, Xiang Jin, Luca Mezincescu, Cosmas Zachos

Physics

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

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)
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	https://doi.org/10.1016/j.physletb.2009.04.019
State	Published - May 18 2009

ASJC Scopus subject areas

Nuclear and High Energy Physics

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title = "Classical and quantal ternary algebras",

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.",

author = "Thomas Curtright and David Fairlie and Xiang Jin and Luca Mezincescu and Cosmas Zachos",

note = "Funding Information: We record our gratitude to J. Nuyts for communicating his 3-on-3-on-3 work to us prior to publication, and for alerting us to Bremner's identity. This work was supported by NSF Award 0555603, and by the US Department of Energy, Division of High Energy Physics, Contract DE-AC02-06CH11357. ",

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AU - Curtright, Thomas

AU - Fairlie, David

AU - Jin, Xiang

AU - Mezincescu, Luca

AU - Zachos, Cosmas

N1 - Funding Information: We record our gratitude to J. Nuyts for communicating his 3-on-3-on-3 work to us prior to publication, and for alerting us to Bremner's identity. This work was supported by NSF Award 0555603, and by the US Department of Energy, Division of High Energy Physics, Contract DE-AC02-06CH11357.

PY - 2009/5/18

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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.

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