On the GNS representation of generalized free fields with indefinite metric

The GNS representation leading to generalized free fields on state spaces with indefinite metric is considered. Along these lines, the domain D of field operators, a fundamental decomposition D = D+ [+̇] D− into positive and negative definite subspaces, and a fundamental symmetry J such that the completed hull K = D∥ · ∥J is a Krein space are explicitely described. These results are finally applied to a rigorous treatment of the charged free fields of mass m > 0.