Quantization of Nambu brackets from operator formalism in classical mechanics

Abstract

This paper proposes a novel approach to quantizing Nambu brackets in classical mechanics using operator formalism. The approach employs the “Planck derivative” to represent Nambu brackets, from which we derive a commutation relation for their quantization. Notably, this commutation relation aligns with that emerging from the T-duality of closed strings in a twisted torus with a B-field, thereby hinting at a potential connection with double field theory.