On the Cones of - and Generalized -Positivity for Quantum Field Theories with Indefinite Metric

  • Gerald Hofmann

    HTWK Leipzig, Germany

Abstract

In order to construct a Krein-space theory (i.e., a -algebra of (unbounded) operators which are defined on a common, dense, and invariant domain in a Krein space) the cones of -positivity and generalized -positivity are considered in tensor algebras. The relations between these cones, algebraic -cones, and involutive cones are investigated in detail.

Furthermore, an example of a -functional defined on (tensor algebra over ) not being -positive and yielding a non-trivial Krein-space theory is explicitely constructed. Thus, an affirmative answer to the question whether or not the method of -functionals (introduced by Ôta) is more general than the one of -positivity (introduced by Jakóbczyk) is provided in the case of tensor algebras.

Cite this article

Gerald Hofmann, On the Cones of - and Generalized -Positivity for Quantum Field Theories with Indefinite Metric. Publ. Res. Inst. Math. Sci. 30 (1994), no. 4, pp. 641–670

DOI 10.2977/PRIMS/1195165793