Higher-order theories from the minimal length

Abstract

We show that the introduction of a minimal length in the context of non-commutative spacetime gives rise (after some considerations) to higher-order theories. We then explicitly demonstrate how these higher-derivative theories appear as a generalization of the standard electromagnetism and general relativity by applying a consistent procedure that modifies the original Maxwell and Einstein-Hilbert actions. In order to set a bound on the minimal length, we compare the deviations from the inverse-square law with the potentials obtained in the higher-order theories and discuss the validity of the results. The introduction of a quantum bound for the minimal length parameter $\sqrt{\beta }$ in the higher-order QED allows us to lower the actual limits on the parameters of higher-derivative gravity by almost half of their order of magnitude.

15 pages

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• Search for Lorentz violation in short-range gravity
• Supersymmetry Breaking as a new source for the Generalized Uncertainty Principle
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Cited by in corpus (7)

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• The generalized uncertainty principle effect in acoustic black holes
• Exotic fermionic fields and minimal length
• Doubly special relativity as a non-local quantum field theory
• The Ultraviolet and Infrared Behavior of an Abelian Proca Model From the Viewpoint of a One-Parameter Extension of the Covariant Heisenberg Algebra
• Thermal effects of a photon gas with a deformed Heisenberg algebra
• From minimal-length quantum theory to modified gravity