Thomas-Fermi theory at the Planck scale: A relativistic approach

摘要

Many quantum gravity theories predict a minimal length of the order of the Planck length. This prescription implies a number of modifications in the phase space structure that have consequences on any statistical mechanics approach. We have recently introduced (Shababi and Ourabah, 2019) a formulation of the Thomas-Fermi model in consistency with the minimal length prescription. Herein we extend our formulation to include relativistic effects. In this occasion, we present a formulation in an N-dimensional space to shed light on the behavior of the different corrections with space dimensionality, and generalize our formulation to include the effect of a very strong magnetic field. To substantiate our point, we apply our model to the screening process and provide estimations of the Fermi length for star interior. (C) 2019 Elsevier Inc. All rights reserved.