Generalized Abelian Deformations: Application to Nambu Mechanics

Abstract

We study Abelian generalized deformations of the usual product of polynomials introduced in hep-th/9602016. We construct an explicit example for the case of $su/2$ which provides a tentative of a quantum-mechanical description of Nambu Mechanics on $R^3$. By introducing the notions of strong and weak triviality of generalized deformations, we show that the Zariski product is never trivial in either sense, while the example constructed here in a quantum-mechanical context is only strongly non-trivial.

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References in corpus (2)

• On Foundation of the Generalized Nambu Mechanics
• Deformation Quantization and Nambu Mechanics

Cited by in corpus (3)

• Classical and Quantum Nambu Mechanics
• A No-Go Theorem for M5-brane Theory
• On generalized Abelian deformations