THE HILBERT SPACE STRUCTURE CONDITION FOR QUANTUM FIELD THEORIES WITH INDEFINITE METRIC AND TRANSFORMATIONS WITH LINEAR FUNCTIONALS

摘要

The sufficient Hilbert space structure condition (abbr. HSSC) ((H) over cap) is introduced such that, if a linear functional T defined on some tensor algebra satisfies ((H) over cap), then the transformed functional p(T)(s) obtained by s-product power series satisfies the usual HSSC. Consequently, the GNS representation with respect to p(T)(s) yields a Krein space as the space of state vectors. This generalizes the sufficient HSSC for truncated Wightman functionals due to Albeverio, Gottschalk and Wu. [References: 25]