A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications

TL;DR

This paper explores a higher order generalized uncertainty principle (GUP) incorporating minimal length and maximal momentum, deriving exact states, extending to multiple dimensions, and analyzing implications for energy spectra, blackbody radiation, and cosmological constant.

Contribution

It introduces a formally self-adjoint, perturbative representation of the GUP, extends it to higher dimensions, and investigates its physical consequences including noncommutative geometry and modified spectra.

Findings

Upper bounds on energy spectra due to maximal momentum

Modification of blackbody radiation at high frequencies

Finite estimation of the cosmological constant

Abstract

In a recent paper, we presented a nonperturbative higher order generalized uncertainty principle (GUP) that is consistent with various proposals of quantum gravity such as string theory, loop quantum gravity, doubly special relativity, and predicts both a minimal length uncertainty and a maximal observable momentum. In this Letter, we find exact maximally localized states and present a formally self-adjoint and naturally perturbative representation of this modified algebra. Then we extend this GUP to D dimensions that will be shown it is noncommutative and find invariant density of states. We show that the presence of the maximal momentum results in upper bounds on the energy spectrum of the free particle and the particle in box. Moreover, this form of GUP modifies blackbody radiation spectrum at high frequencies and predicts a finite cosmological constant. Although it does not solve the cosmological constant problem, it gives a better estimation with respect to the presence of just the minimal length.