Symplectic Quantization of Open Strings and Noncommutativity in Branes

TL;DR

This paper demonstrates how symplectic quantization of open strings with boundary conditions reveals the noncommutative nature of brane coordinates in the presence of a background field.

Contribution

It introduces a method to incorporate boundary conditions as constraints in symplectic quantization, linking string boundary conditions to noncommutative geometry.

Findings

Reproduces noncommutativity of brane coordinates

Translates boundary conditions into symplectic constraints

Provides a new approach to quantize open strings with background fields

Abstract

We show how to translate boundary conditions into constraints in the symplectic quantization method by an appropriate choice of generalized variables. This way the symplectic quantization of an open string attached to a brane in the presence of an antisymmetric background field reproduces the non commutativity of the brane coordinates.