  It is shown that the mixing of ultraviolet and infrared divergences in
quantum field theory on Moyal space is not an artefact of the Euclidean
framework, but occurs also in the Hamiltonian setting when the interaction is
given in terms of the Moyal twisted convolution product. The mixing mechanism
in both settings is examined from the point of view of microlocal analysis and
it is shown that they are different from one another.
