Relativistic Remnants of Non-Relativistic Electrons

Abstract

Electrons obeying the Dirac equation are investigated under the non-relativistic $c\mapsto \infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct{)}^2-x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.

22 pages

References in corpus (4)

• Revisiting Zitterbewegung
• Space-time evolution of Dirac wave packets
• The zig-zag road to reality
• On the zig-zag pilot-wave approach for fermions