Waves on noncommutative spacetimes

Waves on "commutative" spacetimes like R-d are elements of the commutative algebra C-0(R-d) of functions on R-d. When C-0(R-d) is deformed to a noncommutative algebra A(theta)(R-d) with deformation parameter theta (A(0)(R-d)=C-0(R-d)), waves being its elements, are no longer complex-valued functions on R-d. Rules for their interpretation, such as measurement of their intensity, and energy, thus need to be stated. We address this task here. We then apply the rules to interference and diffraction for d 0. As an application, we discuss interference of starlight due to cosmic strings