Quantum hoop conjecture and a natural cutoff for vacuum energy of a scalar field

TL;DR

This paper introduces a quantum hoop conjecture linking a particle's wavelength to its Schwarzschild radius, providing a natural cutoff for scalar field vacuum energy, with implications for quantum gravity and cosmology.

Contribution

It proposes a novel quantum hoop conjecture that establishes a fundamental limit on particle wavelengths, leading to a natural cutoff for vacuum energy calculations.

Findings

Derived an upper bound for particle wave number and momentum.

Provided a natural cutoff for scalar field vacuum energy.

Implications for quantum gravity and cosmological constant problem.

Abstract

We propose here a quantum hoop conjecture which states: the de Broglie wavelength of a quantum system cannot be arbitrarily small, it must be larger than the characterized Schwarzschild radius of the quantum system. Based on this conjecture, we find an upper bound for the wave number (or the momentum) of a particle, which offers a natural cutoff for the vacuum energy of a scalar field.