Equivalence of Locality and Paralocality in Free Parafield Theory

Abstract

It is shown that locality, i.e., vanishing of the commutator at space-like saepration in the parafield Hilbert space $\mathcal{A}$, implies paralocality, i.e., vanishing of the commutator at space-like separation in the larger Green component Hilbert space $\mathcal{B}$. This demonstration removes an unwanted assumption in a recent derivation of parafield selection rules. The method of demonstration yields the general statement that the vacuum is separating for polynomials of localized free parafields in the representation on the space $\mathcal{B}$.