The origin of noncommutativity?

TL;DR

This paper explores the multiple consistent boundary Poisson structures in open string theory with background B-fields, revealing that the noncommutativity of D-branes depends on the chosen Poisson structure.

Contribution

It introduces a new approach showing infinitely many consistent Poisson structures, each leading to different noncommutative properties of D-branes in open string theory.

Findings

Infinitely many consistent Poisson structures exist for open strings with B-fields.

The noncommutativity of D-branes depends on the selected Poisson structure.

Different structures lead to distinct canonical quantizations.

Abstract

Consistent boundary Poisson structures for open string theory coupled to background $B$-field are considered using the new approach proposed in hep-th/0111005. It is found that there are infinitely many consistent Poisson structures, each leads to a consistent canonical quantization of open string in the presence of background $B$-field. Consequently, whether the $D$-branes to which the open string end points are attached is noncommutative or not depends on the choice of a particular Poisson structure.