Invariance under finite conformal transformations in Minkowski space and theWightman axioms imply strong locality (Huygens principle) and rationality ofcorrelation functions, thus providing an extension of the concept of vertexalgebra to higher dimensions. Gibbs (finite temperature) expectation valuesappear as elliptic functions in the conformal time. We survey and furtherpursue our program of constructing a globally conformal invariant model of ahermitean scalar field L of scale dimension four in Minkowski space-time whichcan be interpreted as the Lagrangian density of a gauge field theory.
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