Feynman path summation for the Dirac equation: An underlying one-dimensional aspect of relativistic particle motion

Abstract

It is observed that the Feynman path summation for the one-dimensional Dirac equation can be projected into three spatial dimensions to yield a path-summation formula for physical spin- particles of nonzero mass. Since the three-space projection matrix is independent of time and does not involve the particle's mass, relativistic motion governed by the Dirac equation has an underlying one-dimensional aspect. © 1983 The American Physical Society.