CANONICAL ANALYSIS OF NONCOMMUTATIVITY OF OPEN BOSONIC STRINGS

Abstract

Generally, in the presence of an antisymmetric tensor background field, the open string moving with mixed Neumann and Dirichlet boundary conditions will make the spacetime coordinates noncommutative. In this paper, comparing to the flat and static D-brane case studied in the literature, we first generalize the D-branes to be dynamical. And then by using the Hamiltonian approach, through a calculation of the classical Poisson brackets among the Fourier mode components of the string embedding coordinates and a consistent quantization procedure, we show that the spacetime coordinates of the string endpoints in the directions parallel and perpendicular to the D-branes both become noncommutative.