Higher-order theories from the minimal length

TL;DR

This paper explores how introducing a minimal length in non-commutative spacetime leads to higher-order theories, modifying electromagnetism and gravity, and establishes bounds on the minimal length using experimental deviations.

Contribution

It demonstrates the emergence of higher-derivative theories from minimal length considerations and provides bounds on the minimal length parameter through comparisons with experimental data.

Findings

Higher-order theories naturally arise from minimal length assumptions.

Bounds on the minimal length parameter are established from deviations in inverse-square law.

Quantum bounds significantly tighten constraints on higher-derivative gravity parameters.

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.