Poincare group operators with 4-vector position

Abstract

We present a new set of massless Poincaré group operators Hermitian with respect to the $1/r$ inner product space, which have quasi-plane wave energy-momentum eigenfunctions having velocity $c$ along their axis of propagation. These are constructed by means of a unitary transformation from a known set of massless Poincaré group operators of helicity $s=0,\pm \frac{1}{2},\pm \mathrm{1...}$ The position vector $\mathbf{r}$ is the space part of a null 4-vector.

10 pages, no figures