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Scale-invariant phase space and the conformal group

James T. Wheeler
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Abstract

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.

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James T. Wheeler. 1994-11-11. Scale-invariant phase space and the conformal group. https://arxiv.org/abs/gr-qc/9411030

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