The notion of essential locality for nonlocalizable fields

Abstract

The classification of extension of the field commutator outside the light cone suggested by Constantinescu and Taylor is analyzed and shown to be to a large extent mathematically equivalent to the notion of essential locality, introduced in a recent paper by the present authors. Simple model fields are constructed which disprove the interpretation given by Constantinescu and Taylor. Essential locality is shown to hold for the two-point function of every scalar Hermitian field, including the massless case. It is, moreover, shown to be weaker than locality and independent of the other Wightman axioms. Unfortunately, essential locality turns out to be unstable under limits. In order to indicate the possibility that there are essentially local fields which do not fall into Jaffe’s class and the commutator of which is concentrated in the closed light cone, Jaffe’s concept of strict localizability is generalized. As a by-product it is indicated that local fields (in the generalized sense) may have extreme high energy behavior.