Abstract
The geometric structure of systems which are invariant under the 15-parameter conformal group of the Minkowski space is investigated. In particular, we analyse the action of the group on the compactified Minkowski space M 4 c and the 5-dimensional manifold K 5 ( E, b ) of events E and measuring rods b . The properties of these manifolds as homogeneous spaces and the structure of their tangent and cotangent spaces are disussed, too. Finally, we investigate the notion of causality in the context of a conformally invariant world: we show that it is possible to introduce a conformally invariant local causal structure which is just the same as that of a Poincaré-invariant one in Minkowski space. Globally, this world is highly acausal, because any two points can be connected by timelike curves.
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