  In this paper, we further develop the analysis started in an earlier paper on
the inequivalence of certain quantum field theories on noncommutative
spacetimes constructed using twisted fields. The issue is of physical
importance. Thus it is well known that the commutation relations among
spacetime coordinates, which define a noncommutative spacetime, do not
constrain the deformation induced on the algebra of functions uniquely. Such
deformations are all mathematically equivalent in a very precise sense. Here we
show how this freedom at the level of deformations of the algebra of functions
can fail on the quantum field theory side. In particular, quantum field theory
on the Wick-Voros and Moyal planes are shown to be inequivalent in a few
different ways. Thus quantum field theory calculations on these planes will
lead to different physics even though the classical theories are equivalent.
This result is reminiscent of chiral anomaly in gauge theories and has obvious
physical consequences. The construction of quantum field theories on the
Wick-Voros plane has new features not encountered for quantum field theories on
the Moyal plane. In fact it seems impossible to construct a quantum field
theory on the Wick-Voros plane which satisfies all the properties needed of
field theories on noncommutative spaces. The Moyal twist seems to have unique
features which make it a preferred choice for the construction of a quantum
field theory on a noncommutative spacetime.
