Particle production and transplanckian problem on the non-commutative plane

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.

Minor typos corrected, references added. Accepted for publication by Modern Physics Letter A

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• A new approach to non-commutative inflation
• The entropy of an acoustic black hole in Bose-Einstein condensates
• Hausdorff dimension of a particle path in a quantum manifold
• Minimal Scales from an Extended Hilbert Space
• Finite axionic electrodynamics from a new noncommutative approach
• The entropy of an acoustic black hole in Bose-Einstein condensates: transverse modes as a cure for divergences
• Aspects of Quantum Gravity in Cosmology
• Explosive particle production in non-commutative inflation
• The coordinate coherent states approach revisited