We study the dynamics of an open membrane with a cylindrical topology, in the
background of a constant three form, whose boundary is attached to p-branes.
The boundary closed string is coupled to a two form potential to ensure gauge
invariance. 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, unlike the case of the static gauge, where the
chain has an infinite sequence of terms. It is conjectured that the formulation
of closed string field theory may necessitate introduction of a star product
which is both noncommutative and nonassociative.Comment: 32page