On the Quantization of Nambu Brackets
Hidetoshi Awata, Miao Li, Djordje Minic, Tamiaki Yoneya
TL;DR
This paper introduces new examples of quantum Nambu brackets involving matrices and three-index objects, demonstrating their key properties and discussing potential applications in M-theory.
Contribution
It provides the first non-trivial quantum Nambu brackets satisfying skew-symmetry and the Fundamental Identity, expanding the understanding of quantum Nambu mechanics.
Findings
Examples involve square matrices and three-index objects
They satisfy skew-symmetry and the Fundamental Identity
Potential applications in M-theory are discussed
Abstract
We present several non-trivial examples of the three-dimensional quantum Nambu bracket which involve square matrices or three-index objects. Our examples satisfy two fundamental properties of the classical Nambu bracket: they are skew-symmetric and they obey the Fundamental Identity. We contrast our approach to the existing literature on the quantum deformations of Nambu mechanics. We also discuss possible applications of our results in M-theory.
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