On conformal invariance of interacting fields

We study the action of the conformal algebra on interacting fields. On a certain set of states the algebra is integrated to projective representations ofSU(2,2). These representations are shown to be equivalent to the representations of the interpolated discrete series ofSU(2,2). Using this result we give a formula for the two-point Wightman function for arbitrary spin and dimension of the field. Finally we discuss the limit when the dimension tends to the canonical value.