Nature of the Axioms of Relativistic Quantum Field Theory. I

The formulation of field theories by means of Wightman functions is studied. It is shown that, given two field theories that satisfy all the axioms, one can construct a family of Wightman fields with the same properties by a process of superposition of Wightman functions. The condition of unitarity is formulated without reference to asymptotic conditions, and it is proved that the Wightman fields constructed by the above superposition process (starting with ``unitary'' fields) fail to preserve unitarity, and a fortiori, the standard asymptotic condition.