Physical Sciences and Mathematics Commons^™

Time And Dark Matter From The Conformal Symmetries Of Euclidean Space, Jeffrey S. Hazboun, James Thomas Wheeler

All Physics Faculty Publications

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. We show that the general solution posesses orthogonal Lagrangian submanifolds, with the induced metric and the spin connection on the submanifolds necessarily Lorentzian, 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 exist in this geometry, not present in Riemannian geometry. …