Relativistic dynamical symmetries and dilatations

Publisher Website
Google Scholar
Abstract
Characterizing the state of a relativistic particle by a pair (xμ,ξμ) of 4-vectors, we are led, in a natural way, to a group H5 of canonical transformations which includes the Poincaré group and dilatations. The structure of the group and its induced irreducible unitary representations are explored. It is shown that H5 has a semisimple noncompact subgroup which permits a systematic treatment of exact and of broken dilatation symmetry. The relevance of these ideas to scale dimension and to a new symmetry, scale conjugation, is discussed. As an application, a mass formula is derived from broken dilatation symmetry.