Particle production and transplanckian problem on the non-commutative plane

Understand

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.