Noncommutative fields and the short-scale structure of spacetime

Abstract

There is a growing evidence that due to quantum gravity effects the effective spacetime dimensionality might change in the UV. In this letter we investigate this hypothesis by using quantum fields to derive the UV behaviour of the static, two point sources potential. We mimic quantum gravity effects by using non-commutative fields associated to a Lie group momentum space with a Planck mass curvature scale. We find that the static potential becomes finite in the short-distance limit. This indicates that quantum gravity effects lead to a dimensional reduction in the UV or, alternatively, that point-like sources are effectively smoothed out by the Planck scale features of the non-commutative quantum fields.

12 pages, 2 figures

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• A group theoretic description of the $\kappa$-Poincaré Hopf algebra
• A short introduction to $\kappa$-deformation
• Quantum particles in non-commutative space-time: an identity crisis
• Ultraviolet dimensional reduction of spacetime with zero-point length
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Spinning Toroidal Brane Cosmology; A Classical and Quantum Survey
• Perturbative effective action for the photon in noncommutative QED${}_2$ and exactness of the Schwinger mass
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• One-loop Photon's Effective Action in the Noncommutative Scalar QED${}_3$