Dual-Spin Dirac Equation and Maxwell's Equations

When studying the Dirac equation and Maxwell's equations, replacing the current second-order Pauli spin matrices with fourth-order spin matrices reveals that the Dirac equation contains a pair of spins, and the Maxwell's equations contain spins and Runge-Lenz vector. This book refers to the pair of spins as "dual-spin". The dual-spin matrices are the main components of these equations. Based on the existence of infinite representations of dual-spin matrices, they can be expressed as operators. This book proposes a new representation for Dirac equation and the Maxwell's equations using these dual-spin operators, and mathematically proves its existence. With the new representation, this book also demonstrates the harmonious unity of the internal structure of the equations and the inherent connection between the two equations, and introduces new symmetries, new solution methods, as well as new approaches to Lorentz transformations by this dual-spin representation. Furthermore, the original Dirac equation only contained one spin, but the author has discovered that there are two spins, which is a breakthrough in cognition.