Quantization of Nambu Brackets from Operator Formalism in Classical Mechanics

TL;DR

This paper introduces a new operator-based method for quantizing Nambu brackets in classical mechanics, revealing connections to string theory dualities and potentially advancing the understanding of quantum structures in classical systems.

Contribution

It presents a novel operator formalism for Nambu brackets and links the resulting commutation relations to string theory dualities, offering a new perspective on quantization.

Findings

Derived a commutation relation from the Planck derivative approach

Connected the quantization of Nambu brackets to T-duality in string theory

Suggested a link to Double Field Theory

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.