Interacting fermion–antifermion pairs via Cornell-type coupling in magnetized space–time with a cosmological constant

In this study, we aim to investigate the interaction dynamics of a fermion–antifermion ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>f</mml:mi> <mml:menclose class="tml-overline" notation="top"> <mml:mi>f</mml:mi> </mml:menclose> </mml:mrow> </mml:math> ) pair within a curved three-dimensional space–time with a non-zero cosmological constant ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:mrow> <mml:mo>&gt;</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ). 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mn>4</mml:mn> <mml:mo>×</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:mrow> </mml:math> 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.