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The Hilbert Space Structure Condition for Quantum Field Theories with Indefinite Metric and Transformations with Linear Functionals

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Abstract

The sufficient Hilbert space structure condition (abbr. HSSC) (Ĥ) is introduced such that, if a linear functional T defined on some tensor algebra satisfies (Ĥ), 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.

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  1. Universität Leipzig, Mathematisches Institut, Augustusplatz 10, Leipzig, D-04109, Germany

    Gerald Hofmann

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  1. Gerald Hofmann
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Hofmann, G. The Hilbert Space Structure Condition for Quantum Field Theories with Indefinite Metric and Transformations with Linear Functionals. Letters in Mathematical Physics 42, 281–295 (1997). https://doi.org/10.1023/A:1007393411896

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