Interacting Fermion-Antifermion Pairs via Cornell-Type Coupling in Magnetized Space-Time with a Cosmological Constant

Abstract

In this study, we aim to investigate the interaction dynamics of a fermion-antifermion (f f(-)) pair within a curved three-dimensional space-time with a non-zero cosmological constant (Lambda>0). Our primary goal is to understand the relative motion of this pair by deriving a radial equation set and finding analytical solutions using the covariant many-body Dirac equation. We begin by formulating the relevant equation, which leads to a 4x4 matrix equation governing the motion of the pair. We present a non-perturbative second-order wave equation for the quantum system and demonstrate that it can be solved under the assumption that Lambda is small. This assumption allows us to derive analytical solutions using well-known special functions. Accordingly, we explore the impact of the space-time background on the dynamics of the coupled pairs.