UV divergence-free QFT on noncommutative plane

We formulate noncommutative qauntum field theory in terms of fields defined as mean value over coherent states of the noncommutative plane. No ∗-product is needed in this formulation and noncommutativity is carried by a modified Fourier transform of fields. As a result the theory is UV finite and the cutoff is provided by the noncommutative parameter θ.