Photon velocity, power spectrum in Unruh effect with modified dispersion relation

TL;DR

This paper explores how a new generalized uncertainty principle affects photon velocity and the Unruh effect's power spectrum, revealing energy-dependent superluminal propagation and correcting previous results in the literature.

Contribution

It introduces a novel form of the generalized uncertainty principle with linear and quadratic terms, deriving the modified dispersion relation and analyzing its impact on photon velocity and the Unruh effect.

Findings

Photon velocity becomes energy-dependent and superluminal.

Power spectrum depends on particle energy due to the generalized uncertainty principle.

Corrects previous first-order results in the literature regarding the power spectrum.

Abstract

In this paper we propose a new form of generalized uncertainty principle which involves both a linear as well as a quadratic term in the momentum. From this we have obtained the corresponding modified dispersion relation which is compared with the corresponding relation in rainbow gravity. The new form of the generalized uncertainty principle reduces to the known forms in appropriate limits. We then calculate the modified velocity of photons and we find that it is energy dependent, allowing therefore for a superluminal propagation. We then derive the $1+1$-dimensional Klein-Gordon equation taking into account the effects of the modified dispersion relation. The positive frequency mode solution of this equation is then used to calculate the power spectrum arising due to the Unruh effect. The result shows that the power spectrum depends on the energy of the particle owing its origin to the presence of the generalized uncertainty principle. Our results capture the effects of both the simplest form as well as the linear form of the generalized uncertainty principle and also points out an error in the result of the power spectrum up to first order in the generalized uncertainty principle parameter existing in the literature.