2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119072Conformal theories in a d dimensional spacetime may be expressed as manifestly conformal theories in a d+2 dimensional conformal space as first proposed by Dirac. The reduction to d dimensions goes via the d+1 dimensional hypercone in the conformal space. Here we give a rather extensive expose of such theories. We review and extend the theory of spinning conformal particles. We give a precise and geometrical formulation of manifestly conformal fields for which we give a consistent action principle. The requirement of invariance under special gauge transformations off the hypercone plays a fundamental role here. Maxwell's theory and linear conformal gravity are derived in the conformal space and are treated in detail. Finally, we propose a consistent coordinate invariant action principle in the conformal space and give an action that should correspond to conformal gravity.70 pagesHigh Energy Physics - Theorytext