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Our investigations of conformal invariance are based on the theory of analytic representations of the conformal group and its universal covering group. With its help the action of the conformal group on free massless fields, Greenberg fields, Wick products of these fields, and the Thirring fields is studied. In this context we find an infinite set of new operator solutions for the Thirring model that are all equivalent to each other. Explicit constructions of the nonlocal special conformal transformations of all these fields are given.
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