Particle production and transplanckian problem on the non-commutative
  plane
  We consider the coherent state approach to non-commutativity, and we derive
from it an effective quantum scalar field theory. We show how the
non-commutativity can be taken in account by a suitable modification of the
Klein-Gordon product, and of the equal-time commutation relations. We prove
that, in curved space, the Bogolubov coefficients are unchanged, hence the
number density of the produced particle is the same as for the commutative
case. What changes though is the associated energy density, and this offers a
simple solution to the transplanckian problem.
