On Wick Power Series Convergent to Nonlocal Fields

The infinite series in Wick powers of a generalized free field are considered that are convergent under smearing with analytic test functions and realize a nonlocal extension of the Borchers equivalence classes. The nonlocal fields to which they converge are proved to be asymptotically commuting, which serves as a natural generalization of the relative locality of the Wick polynomials. The proposed proof is based on exploiting the analytic properties of the vacuum expectation values in x-space and applying the Cauchy--Poincare theorem.