The seventh Marcel Grossmann meeting on recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories : 6th Marcel Grossmann meeting : Papers.
The gauge bundle of the 4-dim conformal group over an 8-dim base space, called biconformal space, is shown have a consistent interpretation as a scale-invariant phase space. Specifically, we show that a classical Hamiltonian system generates a differential geometry which is necessarily biconformal, and that the classical Hamiltonian dynamics of a point particle is equivalent to the specification of a 7-dim hypersurface in flat biconformal space together with the consequent necessary existence of a set of preferred curves. The result is centrally important for establishing the physical interpretation of conformal gauging.
Wheeler, J. T., Scale-invariant phase space and the conformal group, Proceedings of the Seventh Marcel Grossmann Meeting on General Relativity , R. T. Jantzen and G. M. Keiser, editors, World Scientific, London (1996) pp 457-459.