Geometrical realization of scalar electrodynamics

The group O(5, 2) can be interpreted as the conformal group acting on a five-dimensional space. Starting with an O(5, 2)-invariant massless scalar theory in seven-dimensional space, we realize one of the O(5, 2) transformations locally by means of a seven-vector field. We then demand that the equations of motion be well defined in the projective five-dimensional space. The equations which result are the usual ones of four-dimensional massive scalar electrodynamics, with one or two intriguing differences.