Timelike and Spacelike Vectors Transform into Null Vectors through Local Gauge Transformations in Particle Physics

We will prove that timelike and spacelike vectors can transform into null vectors through local gauge transformations in four-dimensional Lorentzian spacetimes. It is not possible to transform timelike or spacelike vectors into null vectors through coordinate transformations. We will achieve this goal through local electromagnetic gauge transformations and show examples. It is also possible to achieve this result through local Yang–Mills non-Abelian gauge transformations. We will briefly discuss applications in microparticle physics such as rare decays and the Drell–Yan process.