Photons and tachyons with continuous spin

Abstract

Lightlike and spacelike representations of the Poincaré group, describing photons and tachyons with continuous spin, are considered. We examine the conditions under which these representations can assume a form analogous to the Shirokov-Foldy form for the timelike representations, namely a form in which the generators of the appropriate little group show no mixing of the momentum and internal degrees of freedom. While every continuous spin lightlike representation can be put into this form, only those spacelike ones can, which correspond to using a continuous series representation of the little group appropriate to this case.