Non-Abelian Extensions of the Dirac Oscillator: A Theoretical Approach

Abstract: This paper presents a mathematical formulation of the Dirac oscillator within a non-Abelian gauge field. The Dirac equation, a fundamental equation in relativistic quantum mechanics, has been modified to include interactions with non-Abelian gauge fields governed by Lie groups, such as SU(2). This theoretical framework aims to capture the complex quantum dynamics arising from these interactions. We derive the interaction terms and provide a comprehensive description of the modified Dirac oscillator by integrating concepts from both Abelian and non-Abelian interactions. The primary contributions of this work include introducing additional interaction terms in the Hamiltonian and formulating non-Abelian electromagnetic tensors. These findings pave the way for exploring quantum systems influenced by non-Abelian gauge fields, with potential applications in quantum field theory and particle physics.