By exploiting the boundary state formalism we obtain the string correlator
between two internal points on the one loop open string world-sheet in the
presence of a constant background B-field. From this derivation it is clear
that there is an ambiguity when one tries to restrict the Green function t
o the boundary of the surface. We fix this ambiguity by showing that there
is a unique form for the correlator between two points on the boundary whic
h reproduces the one loop field theory results of different noncommutative
field theories. In particular, we present the derivation of one loop diagra
ms for phi(6)(3) and phi(4)(4) scalar interactions and for Yang-Mills theor
y. From the 2-point function we are able to derive the one loop beta-functi
on for noncommutative gauge theory. (C) 2000 Elsevier Science B.V. All righ
ts reserved.