Abstract
The connected symmetry group SU(2, 2) of twistor space (T), a four-dimensional complex manifold with metric dsT2≡dX0 dX2¯+dX2 dX0¯+dX1 dX3¯+dX3 dX1¯,and the connected symmetry group O0(2, 4) of conformal space (C), a six-dimensional real manifold with metric dsC2≡(dX0)2−(dX1)2−(dX2)2−(dX3)2−(dX4)2+(dX5)2,are 4:1 and 2:1 homomorphic, respectively, to the restricted conformal group in compactified Minkowski space M. We obtain explicit realizations for these homomorphisms and explore the invariant geometrical relationships they imply between T, C, and M. As an application of the twistor formalism, we show that every continuous conformal transformation has a unique decomposition as the product of a Lorentz transformation, a translation, an acceleration, a dilation, and one of four special conformal transformations.
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