Noncommutative open strings from Dirac quantization

TL;DR

This paper applies Dirac constraint quantization to D-branes with a constant B-field, resolving previous ambiguities and deriving noncommutative coordinates consistent with conformal field theory results.

Contribution

It provides a rigorous derivation of noncommutative coordinates on D-branes using Dirac quantization, clarifying subtleties in earlier analyses.

Findings

Derivation of noncommutative coordinates consistent with conformal field theory

Identification of subtle issues in previous constraint analyses

New commutator relations among canonical variables

Abstract

We study Dirac commutators of canonical variables on D-branes with a constant Neveu-Schwarz 2-form field by using the Dirac constraint quantization method, and point out some subtleties appearing in previous works in analyzing constraint structure of the brane system. Overcoming some ad hoc procedures, we obtain desirable noncommutative coordinates exactly compatible with the result of the conformal field theory in recent literatures. Furthermore, we find interesting commutator relations of other canonical variables.