Quantum-gravitational corrections to the hydrogen atom and harmonic oscillator

TL;DR

This paper compares quantum-gravitational corrections to simple quantum systems from space-time dimension reduction and minimum-length quantum mechanics, finding similar magnitudes but opposite signs in energy shifts, highlighting the concept's significance.

Contribution

It demonstrates that quantum-gravitational corrections from space-time dimension reduction align with those from minimum-length quantum mechanics, emphasizing the concept's physical relevance.

Findings

Corrections from both approaches are of similar magnitude.

The sign of energy shifts differs between the two methods.

Total correction sign remains uncertain due to opposing contributions.

Abstract

It is shown that the rate of corrections to the hydrogen atom and harmonic oscillator due to profound quantum-gravitational effect of space-time dimension running/reduction coincides well with those obtained by means of the minimum-length deformed quantum mechanics. The rate of corrections are pretty much the same within the accuracy by which we can judge the quantum-gravitational corrections at all. Such a convergence of results makes the concept of space-time dimension running more appreciable. As a remarkable distinction, the energy shift due to dimension reduction has the opposite sign as compared with the correction obtained by means of the minimum-length modified quantum mechanics. Thereby, the sign of total quantum-gravitational correction remains obscure.