Exploring Statistical Properties of Fermion-Antifermion Pairs in Magnetized Spacetime under Non-Zero Cosmology

Abstract

This research investigates the complex statistical behavior of fermion-antifermion pairs within a (2+1)-dimensional magnetized Bonnor-Melvin background affected by non-zero cosmological conditions. The Bonnor-Melvin magnetic universe model, known for its cylindrical symmetry, preserves the invariance of quantum field dynamics under Lorentz boosts along the z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z$$\end{document}-axis. This framework facilitates the examination of (2+1)-dimensional scenarios, where the corresponding spacetime background is identified as the Bonnor-Melvin magnetic 2+1+0-brane solution within the realm of gravity coupled with nonlinear electrodynamics. Initially, the precise energy spectra of these pairs are summarized using an analytical solution derived from the fully covariant two-body Dirac equation. Subsequently, the statistical properties inherent in these pair formations are investigated. These findings may illuminate the interplay among magnetic fields, spacetime geometry, and the cosmological constant, thereby enhancing our comprehension of the fundamental behaviors of fermions amidst intricate cosmological conditions. It is anticipated that this investigation could offer new insights into the statistical attributes of fermion-antifermion systems. All thermal characteristics, including free energy, total energy, entropy, and specific heat, have been computed. The impact of diverse factors, such as magnetic fields, spacetime geometry, and the cosmological constant, on these characteristics has been scrutinized.