Field product renormalization and Wilson-Zimmermann expansion in a class of model field theories

A renormalization method is proposed for field operator products at the same points by a limiting procedure, a rigorous investigation of it in a class of field-theoretical models presented and its connection with the Wilson-Zimmermann expansion discussed. Within the models existence and self-adjointness of the renormalized fields is proved, expressions for their matrix elements determined, cyclicity of the vacuum with respect to any odd renormalized-field power shown and the renormalization carried over to define functions of the field. Then a Wilson- Zimmermann-type expansion for field products at short distances is established. It is shown that the field associated with the leading singularity coincides with the renormalized-field power of the limiting process. (19 refs).