We prove that if the out field or the S matrix is expanded in terms of normal ordered products of the in field, then either the expansion has infinite degree or it is the trivial case Aout=Ain, S=1. From this fact it follows that any field theory model in which the Heisenberg field (local or not) has a terminating normal ordered expansion in terms of a (generalized) free field cannot provide a nontrivial unitary S matrix.
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O. W. Greenberg (1962) studied this question.
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