Fermion-Antifermion Pairs in a Magnetized Space-Time with Non-Zero Cosmological Constant

Abstract

We analyze a fermion-antifermion pair within the (2+1) -dimensional Bonnor-Melvin magnetic (BMM) spacetime featuring a nonzero cosmological constant (Lambda > 0). To do this, we rigorously investigate analytical solutions to the corresponding form of a fully -covariant two -body Dirac equation. We derive a non-perturbative wave equation and obtain an exact closed -form analytical solution for the system under consideration. In this magnetic background spacetime, described by a surface with positive Gaussian curvature, we noticed that fermion-antifermion pairs display a collective behavior resembling that of a single quantum oscillator, carrying a total rest mass of the particles and oscillating with a frequency (omega(o) proportional to Lambda), even in the absence of mutual interaction between the particles. This indicates a compelling correlation between the cosmological constant and the energy spectrum of fermion-antifermion systems, implying connections between quantum realms and cosmology.