Local commutativity for nonlocalisable fields

A definition of local commutativity for nonlocalisable field theory is given by means of a limiting procedure for the Wightman functions of the theory; it includes, as a special case, rational functions of the free field. Fields for which this limiting procedure is defined are shown to satisfy many of the desirable features of localisable fields, including the existence of a TCP operator,the clustet property, the existence of asymptotic limits, and the LSZ reduction formulas. A strengthening of the procedure allows forward scattering dispersion relations to be obtained; the effects of nonlocalisibility on rigorous high energy bounds is also considered.