On quasi-free polylocal fields and fields of infinite spin

Abstract We give a method for constructing polylocal fields (depending on many space-time variables) similar to the generalized free field in one variable. The fields satisfy all the axioms given in a previous paper. A special case of the polylocal field may be said to correspond to a local field of infinite spin. The one-particle state of such a theory is infinitely degenerate unless the “one-particle unitarity condition” holds. In certain cases the existence of localized von Neumann algebras (Haag-Araki algebras) can be proved. The “spacelike” asymptotic condition in the form suggested by Haag and Ruelle holds, and so we may expect the interpretation of the theory in terms of asymptotic states.