Fermion-antifermion pairs in Bonnor-Melvin magnetic space-time with non-zero cosmological constant

TL;DR

This paper investigates the behavior of fermion-antifermion pairs in a magnetized universe with a cosmological constant, deriving exact solutions and revealing links between quantum systems and cosmological parameters.

Contribution

It provides the first exact analytical solutions for the two-body Dirac equation in Bonnor-Melvin spacetime with a cosmological constant, highlighting quantum-cosmological connections.

Findings

Exact radial solutions for fermion-antifermion pairs in BMM spacetime.

Discovery of parallels between quantum oscillators and cosmological effects.

Correlation between cosmological constant and fermion energy spectra.

Abstract

We study the relativistic dynamics of fermion-antifermion pairs in the Bonnor-Melvin magnetic (BMM) spacetime in non-zero cosmology. We focus on the $(1+2)$-dimensional cylindrically symmetric BMM-spacetime background. Within the context of such a magnetized universe, we rigorously investigate the fully-covariant two-body Dirac equation. We derive the corresponding radial part of the equation and obtain an exact closed form analytical solution for the problem at hand. Moreover, we report some intriguing parallels with relativistic and non-relativistic quantum oscillators in flat spaces. Notably, our findings suggest a compelling correlation between the cosmological constant and the energy spectrum of fermion-antifermion systems, hinting at profound connections between quantum realms and cosmology.