Particle production and transplanckian problem on the non-commutative plane

TL;DR

This paper develops an effective quantum scalar field theory on a non-commutative plane, showing that while particle production remains unchanged, the energy density is modified, providing a potential solution to the transplanckian problem.

Contribution

It introduces a coherent state approach to non-commutativity and demonstrates its impact on quantum field theory and the transplanckian problem in curved spacetime.

Findings

Particle production rate remains unchanged in non-commutative space.

Energy density associated with particle production is modified.

Provides a simple solution to the transplanckian problem.

Abstract

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.