Quantum Equations of Motion and the Geometrical Imperative II: Relativistic

Abstract

We extract the square root of the Minkowski metric using Dirac/Clifford ma- trices. The resulting 4 × 4 operator dS that represents the square root, can be used to transform four vectors between relatively moving observers. This effects the usual Lorentz transformation. In addition it acts on a Dirac bi-spinor. The operator can be used as a Hamiltonian operator to write an equation of motion for a relativistic spinor. This turns out to be the Dirac equation for electrons in standard form, which appears as a transformation of a moving spinor to the rest frame of the spinor. This approach was introduced in paper I of this series for non relativistic spinor particles. We believe that is is a new approach to familiar results.