On Wick Power Series Convergent to Nonlocal Fields

TL;DR

This paper demonstrates that certain Wick power series of generalized free fields converge to nonlocal fields with asymptotic commutativity, extending the concept of locality in quantum field theory through analytic and complex analysis methods.

Contribution

It introduces a novel convergence result for Wick power series to nonlocal fields and generalizes the notion of locality via asymptotic commutativity using analytic techniques.

Findings

Wick power series converge to nonlocal fields under analytic smearing.

The nonlocal fields exhibit asymptotic commutativity, extending locality concepts.

The proof utilizes the analytic properties of vacuum expectation values and the Cauchy--Poincare theorem.

Abstract

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.