Jeffrey S Hazboun, James T Wheeler
The quotient of the conformal group of Euclidean 4-space by its Weyl subgroup results in a geometry possessing many of the properties of relativistic phase space, including both a natural symplectic form and non-degenerate Killing metric. When we complete the identification with phase space by requiring the existence of orthogonal, canonically conjugate, metric submanifolds, we find that the induced metric and the spin connection are Lorentzian on the submanifolds, despite the Euclidean starting pont. By examining the structure equations of the biconformal space in an orthonormal frame adapted to its phase space properties, we also find that two new tensor fields emerge from this geometry. The first is a combination of the scale factor on the metric with the Weyl vector. The second comes from the components of the spin connection, symmetric with respect to the new metric. Though this field comes from the spin connection it transforms homogeneously.
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http://arxiv.org/abs/1305.6972
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