Particle production and transplanckian problem on the noncommutative plane

We consider the coherent state approach to noncommutativity and we derive from it an effective quantum scalar field theory. We show how the noncommutativity can be taken into account by a suitable modification of the KleinGordon product, and of the equal-time commutation relations. We prove that, in curved space, the Bogoliubov 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. © 2010 World Scientific Publishing Company.