An innovative model for coupled fermion-antifermion pairs

TL;DR

This paper introduces a new theoretical model for fermion-antifermion pairs using the many-body Dirac equation with a position-dependent mass, providing exact solutions for Coulomb-like and Cornell potentials and offering insights into various physical systems.

Contribution

The study develops a novel many-body Dirac model with effective mass modifications, deriving exact energy expressions for fermion-antifermion pairs under different interaction potentials.

Findings

Model matches known Coulomb energy eigenvalues without approximation.

Derived closed-form energy expressions for Cornell potential.

Applicable to diverse fermion-antifermion systems like positronium and excitons.

Abstract

Understanding the behavior of fermion-antifermion (\(f\overline{f}\)) pairs is crucial in modern physics. These systems, governed by fundamental forces, exhibit complex interactions essential for particle physics, high-energy physics, nuclear physics, and solid-state physics. This study introduces a novel theoretical model using the many-body Dirac equation for \(f\overline{f}\) pairs with an effective position-dependent mass (i.e., \(m \rightarrow m + \mathcal{S}(r)\)) under the influence of an external magnetic field. To validate our model, we show that by modifying the mass with a Coulomb-like potential, \(m(r) = m - \alpha/r\), where \(-\alpha/r\) is the Lorentz scalar potential \(\mathcal{S}(r)\), our results match the well-established energy eigenvalues for \(f\overline{f}\) pairs interacting through the Coulomb potential, without approximation. By applying adjustments based on the Cornell potential (i.e., \(\mathcal{S}(r) = kr - \alpha/r\)), we derive a closed-form energy expression. We believe this unique model offers significant insights into the dynamics of \(f\overline{f}\) pairs under various interaction potentials, with potential applications in particle physics. Additionally, it could be extended to various \(f\overline{f}\) systems, such as positronium, relativistic Landau levels for neutral mesons, excitons in monolayer transition metal dichalcogenides, and Weyl pairs in monolayer graphene sheets.