Noncommutativity of Boundary Closed String Coordinates for an Open Membrane on p-Brane

TL;DR

This paper investigates the noncommutative properties of boundary string coordinates of an open membrane with cylindrical topology in a constant three-form background, using Hamiltonian formalism.

Contribution

It introduces a Hamiltonian approach to analyze boundary coordinate noncommutativity for open membranes, extending previous work on string noncommutativity to membrane systems.

Findings

Boundary string coordinates exhibit noncommutativity.

Finite chain of constraints is obtained with a specific gauge.

Method extends noncommutative analysis to membrane dynamics.

Abstract

We study the dynamics of an open membrane with a cylindrical topology, in the background of a constant three form. We use the action, due to Bergshoeff, London and Townsend, to study the noncommutativity properties of the boundary string coordinates. The constrained Hamiltonian formalism due to Dirac is used to derive the noncommutativity of coordinates. The chain of constraints is found to be finite for a suitable gauge choice.