Quantization of Nambu Brackets from Operator Formalism in Classical Mechanics

The quantization of Nambu brackets is formulated using the approach of quantum mechanical formulation of classical mechanics. It is shown that the quantum-momentum operator is defined by the commutation relation between two variables in Nambu dynamics and that the canonical commutation relation between the quantum-position operator and the momentum operator is a natural extension of the Bohr-Sommerfeld quantization for the phase space in Nambu dynamics. As a concrete example, the Nambu dynamical system of membranes is constructed, and its quantization is discussed.Comment: 12 page