Open Wilson Lines and Generalized Star Product in Noncommutative Scalar Field Theories

Open Wilson line operators and generalized star product have been studied extensively in noncommutative gauge theories. We show that they also show up in noncommutative scalar field theories as universal structures. We first point out that dipole picture of noncommutative geometry provides an intuitive argument for robustness of the open Wilson lines and generalized star products therein. We calculate one-loop effective action of noncommutative scalar field theory with cubic self-interaction and show explicitly that the generalized star products arise in the nonplanar part. It is shown that, at low-energy, large noncommutativity limit, the nonplanar part is expressible solely in terms of the {\sl scalar} open Wilson line operator and descendants.