Quantum equations of motion and the geometrical imperative: relativistic

Abstract

We extract the square root of the Minkowski metric using Dirac/Clifford matrices. 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 is essentially a Hamiltonian that can be used to write an equation of motion for a relativistic spinor. This turns out to be the Dirac equation for electrons in standard form. We believe that it is a new approach to familiar results.