Open membranes, p-branes and noncommutativity of boundary string coordinates

We study the dynamics of an open membrane with a cylindrical topology, in t he background of a constant three form, whose boundary is attached to p-bra nes. The boundary closed string is coupled to a two form potential to ensur e gauge invariance. We use the action, due to Bergshoeff, London and Townse nd, to study the noncommutativity properties of the boundary string coordin ates. The constrained hamiltonian formalism due to Dirac is used to derive the noncommutativity of coordinates. The chain of constraints is found to b e 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 t he formulation of closed string field theory may necessitate introduction o f a star product which is both non commutative and non associative.