Zero-mass fermion wavepackets

Abstract

Abstract Localized spinor solutions of the zero-mass free-space Dirac equation, which are eigenstates of the angular momentum component along the direction of propagation, satisfy the three-dimensional wave equation. General expressions for and special compact forms of space-time localized spinors are given. An exact evaluation of the norm, energy, momentum, and angular momentum of such wavepackets is made. These are all finite. The integrals of the densities over all space, at fixed time, are shown to be equivalent to integrals over the wavenumber weight function. The localized wavepackets converge onto or diverge from a focal region, and their net momentum is smaller than their energy divided by the speed of light. They can be transformed to a (net) zero-momentum frame.