On the Particle and Field nature of $\gamma^\mu$ matrices in the Dirac Equation and the Nature's intrinsic fifth force

Abstract

The Dirac equation is a cornerstone of modern particle physics, which integrates special relativity and quantum mechanics into a consistent framework, yielding the prediction of electron and its antiparticle counterpart, positron. The Dirac equation also lays the foundation of quantum electrodynamics, such that QED phenomenon is supported by fundamental Dirac Algebras calculation. In this article, we will introduce new perspectives of the $\gamma^\mu$ matrix in the Dirac Algebra, by realizing the $\gamma^\mu$ matrices are actual formal quantum fields, the excitation of $\gamma^\mu$ fields correspond to a new particle with both boson and fermion nature. Thus, we show that $\gamma^{\mu}$ is a particle in nature, and can be referred as the nature's intrinsic fifth force. The $\gamma^\mu$ field also serves as the boson-fermion connector in QED interaction.