On the Locality Ideal In the Algebra of Test Functions for Quantum Fields
Jakob Yngvason · Publications of the Research Institute for Mathematical Sciences · 1984
Some basic properties of the locality ideal in Borchers's tensor algebra are established. It is shown that the ideal is a prime ideal and that the corresponding quotient algebra has a faithful Hilbert space representation. A topology is determined for which the positive cone in the quotient algebra is normal, and it is shown that every n -point distribution satisfying the locality condition is a linear combination of positive functional which also satisfy that condition.