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.

Additional references

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• Multi-operator brackets acting thrice
• Ternutator Identities
• Correlators in the supereigenvalue model in the Ramond sector
• On q-deformed infinite-dimensional n-algebra
• (p,q)-deformed Virasoro-Witt n-algebra
• Necessary conditions for Ternary Algebras
• 3-Algebraic structures of the quantum Calogero-Moser model
• On $W_{1+\infty }$ 3-algebra and integrable system
• One-loop Renormalized Coefficient of Noncommutative Supersymmetric Yang-Mills-Chern-Simons Gauge Theories in Three Dimensions