An Innovative Model for Coupled Fermion-Antifermion Pairs

Abstract

Understanding the behavior of fermion-antifermion (ff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\overline{f}$$\end{document}) 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 ff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\overline{f}$$\end{document} pairs with an effective position-dependent mass (i.e., m -> m+S(r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m \rightarrow m + \mathcal {S}(r)$$\end{document}) 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m(r) = m - \alpha /r$$\end{document}, where -alpha/r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\alpha /r$$\end{document} is the Lorentz scalar potential S(r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {S}(r)$$\end{document}, our results match the well-established energy eigenvalues for ff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\overline{f}$$\end{document} pairs interacting through the Coulomb potential, without approximation. By applying adjustments based on the Cornell potential (i.e., S(r)=kr-alpha/r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {S}(r) = kr - \alpha /r$$\end{document}), we derive a closed-form energy expression. We believe this unique model offers significant insights into the dynamics of ff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\overline{f}$$\end{document} pairs under various interaction potentials, with potential applications in particle physics. Additionally, it could be extended to various ff\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\overline{f}$$\end{document} systems, such as positronium, relativistic Landau levels for neutral mesons, excitons in monolayer transition metal dichalcogenides, and Weyl pairs in monolayer graphene sheets.