TY - JOUR

T1 - Classical and quantal ternary algebras

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

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.

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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 -