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 -