A Detailed Analysis of the Quantum Relativistic Motion of an Electron

Based on Pauli spin matrices, this paper settles the geometry of our previously constructed combined spacetime 4-manifold to be {(t+ti, x+yi, y+zi, z+xi): (t,x,y,z) of Minkowski space} locally. Thereby we specify the motions of the two eigenvectors of the spin operator and show that they satisfy Dirac equation of a free electron; accordingly, an electron is a point particle born out of a spinning classic electric field with each of its energy density points rotating along two perpendicularly connected semi-circles. We also demonstrate the pair-annihilation process via a simple trigonometric identity, and we conclude with some pertinent remarks.