Newton Law in Brane-World Scenario with 4d Induced Gravity: Singular Quantum Mechanical Approach

TL;DR

This paper uses a quantum mechanical approach to analyze gravity in brane-world models, showing how the Newtonian potential transitions between 4d and 5d behaviors depending on the distance scale.

Contribution

It introduces a novel quantum mechanical method to study gravity in brane-world scenarios with induced gravity, revealing the potential's behavior across different distance ranges.

Findings

Reveals transition from 4d to 5d Newton potential at specific distances.

Demonstrates energy-dependent coupling affects boundary conditions in quantum models.

Confirms the approach with a simple 1d model.

Abstract

From the viewpoint of the singular quantum mechanics the effect of the energy-dependent coupling constant for $\delta$-function potential is examined. The energy-dependence of the coupling constant naturally generates the time-derivative in the boundary condition of the Euclidean propagator. This is explicitly confirmed by making use of the simple 1d model. The result is applied to the linearized gravity fluctuation equation for the brane-world scenario with 4d induced gravity. Our approach generates $5d$ Newton potential at a certain intermediate range of distance between two test massive sources. For other range of distance 4d Newton potential is recovered.