Two Folk Lemmas on the Expansion of the S Matrix or the Out Field in Normal Ordered In Fields
Oscar Wallace Greenberg · Journal of Mathematical Physics · 1962
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.